It is the inherent nature of all things that they are a compilation of two different and distinct things. It is axiomatic that these two things are space and value. The value of any given thing being what it is, while the space is what it occupies.
It is true that, abstract or otherwise numbers are a thing, therefore they must also contain a compilation of space and value. It is an axiomatic truth that space is the labeling of quantities of dimensions. It is an axiomatic truth that value is the labeling of quantities of existence, other than dimensions.
It is an axiomatic truth that space and value exist in one of two forms. So that any given quantity of space or value is first labeled as defined or undefined. It is reasonable to say that any given number, that has had both its quantities of space and value labeled as undefined, requires no further question as to its nature. If however a given number, has had both its quantities of space and value labeled as defined, it is then necessary to further define the given quantities. That is to say what is the nature of the space and value’s that are defined.
There are four axiomatic steps in the further defining of a defined quantity of space and value. First it is that, after a given quantity of space and value is labeled as defined, a symbol is given to identify the amount of quantities given. Second it is that the given amounts of defined space and value are labeled as finite or infinite. Third it is that the given amounts of defined space and value, that are finite or infinite, are labeled as small or large. Fourth it is that the given amounts of defined space and value, that are finite or infinite, small or large, are labeled as positive or negative.
It is the case that all forms of the defining of quantities of space and value, are from the perspective of our humanity. This then shows that there is a collection of only four kinds of numbers. That is there are numbers that possess an undefined space and an undefined value. Otherwise represented as a ( Uv + Us ). Such a number not requiring further defining. There are numbers that possess a defined value and a defined space. Otherwise represented as a ( Dv + Ds ). Such a number requiring further defining. There are numbers that possess a defined value and an undefined space. Otherwise represented as a ( Dv + Us ). There are numbers that possess an undefined value and a defined space. Otherwise represented as a ( Uv + Ds ).
It is reasonable to say that natural numbers have both their quantities of space and value labeled as defined. That is that a natural number is a ( Dv + Ds ). It is then through the process of further defining, that a natural number such as 2 is labeled as having ( 2Dv + 2Ds ). The symbol 2 then is the symbol identifying the amounts of quantities contained. It is then that the given quantities are labeled as finite. Otherwise represented as a ( 2DvF + 2DsF ). It is then that the given quantities are labeled as large. Otherwise represented as a ( 2DvFL + 2DsFL ). It is then that a positive is assigned to the compilation of space and value, and it is so on for any natural number.
It is also the case that fractions are labeled as a ( Dv + Ds ). That is any given fraction has both its quantities of space and value labeled as defined. So that such a number as .2 is labeled as ( 2DvFS + 2DsFS ). Then a positive is assigned to the compilation of space and value. Additionally a fractional symbol may replace the decimal symbol.
It is also the case that infinite numbers are labeled as a ( Dv + Ds ). So that such a number as 2infinite is defined as a ( 2DvIL + 2DsIL ). As well as fractional infinites such as .2infinite. Which is labeled as ( 2DvIS + 2DsIS ). Then a positive is assigned to both compilations of space and value, and it is so on for any infinite or fractionally infinite number.
Remaining are numbers that are a ( Uv + Ds ) and numbers that are a ( Dv + Us ). Such numbers do not necessarily require further defining. As an undefined quantity of space or value composites the given number. So then such numbers can only be limitedly defined relative to the given defined quantity. If then a number possess a defined value and an undefined space, the sum is then relative to the defined value. So that such a number as ( Dv + Us ) is then a 1 relative. Otherwise represented as a 1r.
If then a number possess an undefined value and a defined space, the sum is then relative to the defined space. So that such a number as a ( Uv + Ds ) is then a zero. As no quantity of value is defined, and as one quantity of space is defined. The space of zero is clearly defined on any number line. The equation ( 1 + (-1) = 0 ) proves this in that, if zero did not occupy a defined space on the number line, then the equation would equal ( -1 ), and not zero.
It is the case in multiplication and division, that neither number given is an actual number. Not in the fashion that each symbol contains both space and value. It is that one symbol is representing a value, and that one symbol is representing a space. It is the case that in multiplication the labeling of the given symbols as space or value in a specific order is not necessary. The sum yielded is always the same.
It is the case that in division the labeling of the given symbols as space or value in a specific order changes the sum that is yielded. So that as an axiom the first given symbol is labeled as value, while the second given symbol is labeled as space.
It is then that in multiplication the given value is placed additionally into the given spaces. Then all values are added in all spaces. It is then that in division the given value is placed divisionally into all given spaces. Then all values are subtracted except one.
So that in the equation ( 2 x 0 = X ), there is a given defined value of ( 2DvFL ), that is placed additionally into the given defined space of ( Ds ). Then all values are added in all spaces. This process then yields the number 2.
Where as the equation ( 0 x 2 = X ), there is a given undefined value of ( Uv ), that is placed additionally into the defined space of ( 2DsFL ). Then all values are added in all spaces. This process then yields the number zero.
So then in the equation ( 2 / 0 = X ), there is a defined value of ( 2DvFL ), that is placed divisionally into the defined space of ( Ds ). Then all values are subtracted except one. This process then yields the number 2.
Where as the equation ( 0 / 2 = X ), there is an undefined value of ( Uv ), that is placed divisionally into the defined space of ( 2DsFL ). Then all values are subtracted except one. This process then yields the number zero.
As an addition to all current field axioms these ideas are expressed as stated.
" For every A in S there exists a Z1 and Z2, constituting A, such that any A in operation of multiplication or division is only representing Z1 or Z2 in any given equation. Such that Z1 for all A’s other than zero equal A. Such that Z2 for all A’s other than zero equal A. Such that Z1 for zero equals zero. Such that Z2 for zero equals 1. "
It is possible that further defining of the given defined value of a relative number, and the given defined space of a zero, is applicable and necessary. It is possible to either leave the same, or adapt exponents and logarithms. Naturally further axioms will be needed for adaption. Such as exponents of zero existing as a space representation of zero (z2). Logarithms of zero existing as a value representation of zero (z1).
It is possible to here-in re-address the idea of the continuum theory. If the defenitions for numbers and their groups, are adapted as stated, and with further exploration into the defining of ( Dv + Us ) relative numbers, ( Uv + Ds ) zero numbers, ( Uv + Us ) undefined numbers, and their placement onto the number line. The idea here being to show all numbers originating from and returning to ( Uv + Us ) on any given number line.
Hmm… well, okay… if you choose to think of it that way.
“Value” huh … hmmm… that might be a poor choice of word. Perhaps “substance”?
Ummm… no. Concepts do not occupy space. Numbers are concepts, specifically of sets. Any given real set might occupy space, but the concept of it being a set certainly doesn’t.
Well, I understand what you meant … despite what you said.
I’m not following what “labelled as defined” is supposed to mean.
James S Saint
Thank you for your time. I will try to respond to all five quotes you posed specifically.
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Axioms are defined as a “self evident” truth. It is that I “inherently” think of these things in this way.
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I prefer value to substance, but I am open to debate on this issue. Have you reasoning on your favor in this issue.
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Abstraction exists for a fact. Such as love, hate, math. I can not touch these things, therefore, yes they are not empirical, but we know they exist because of the consequences of their existences. If then they exist, then they contain space. It is just that “the” space in question is not “definable” by my perspective. ( ie. The “space” of Any given thought is the space of the neurons firing, giving rise to the thought to begin with. Such as the space of love is the space of the chemical giving rise to it’s existences.)
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I’m not sure what you mean here. I meant both sentence to be actual definition’s for space, and for value. I would suppose to you that no more accurate, or short, definition works for either.
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I mean to say exactly as the words mean. Any given thing is either defined or undefined. You either have the ability to “measure, label, and describe” something or you do not.
“Value” is a relative term associated with worth. It implies a subjective usefulness for someone.
“Substance” is more general referring to any physical material.
I didn’t disagree that they existed, only that they occupy space.
I can’t agree with that “axiom”. It is not inherently obvious and frankly, I’m pretty certain that it just isn’t true. Concepts “exist” in the Conceptual/Divine/Ideal realm, not the Physical realm. They are changeless whereas physical existences (in the Physical Realm) are always undergoing change. What we call “space” is merely our means of categorizing physical existence. But we can’t say that there are a stack of number 2’s right over there on the second shelf beside the can of tuna. We can say that “a symbol for the quantity two” is written over there, but that is a different matter. Symbols for concepts are physical.
If something is not at all definable, it doesn’t exist. How can you even talk about something that has no definition? What would you be talking about? That is like arguing whether God exists when you don’t even know what a god is. Words are meaningless, referring to nothing, if they don’t have a definition.
“space is the labeling of quantities of dimensions”
What does that mean??
Quantities of dimensions getting labeled. That sounds like an action, not a thing.
As stated earlier, if a “thing” has no definition, it doesn’t exist. If a word has no definition, it is meaningless (because the definition is the meaning). If you simply haven’t gone to the trouble of spelling out a definition for a thing, then it can still exist, but you can’t talk about it because no one would know what you are saying.
James S Saint
Thank you for your reply
I will start by jokingly suggesting that you don’t watch much sci-fi. Mankind, in his travels, has often come across things that we could not define, yet were entirely real. Further Love, Hate, Math, is not completely undefinable. They are defined with great detail in value, but have little detail in space. I stated clearly in the original post that anything that had undefined value and undefined space does not need to be “talked” about. However numbers…including zero…do not fall under this category. What I am talking about is division and multiplication by zero. And from a philosophical point…the mathematical proof…that “nothing” does NOT exist. I say to you that clearly we could bicker on definitions for space and for value. But I ask you…Is it not the case in all definitions given by you, that an “act” of “labeling” has occurred. That “act of labeling” was either in regards to a value or a dimension. Consciousness is an action. Value, nor Space, exists without consciousness measuring, defining, “labeling” quantities of it. For example the “law of the observer.”. Granted our knowledge of QM is not currently complete.
I’m just one of those who can watch sci-fi without believing any of it to be real. 
You are conflating things that cannot be defined with things that merely haven’t been defined well because they are difficult to define.
Perhaps that’s because they have nothing to do with space?
That might depend upon why it doesn’t have a definition.
True, numbers are symbols (“words”) that have been well defined and are void of space.
Yeah, we could, but then again, we could perhaps come to agreement.
I wouldn’t argue with that.
Actually definitions are in regards to words (including numbers). A definition is merely a description of a concept, usually including an associated word.
Emm… not really. In English just about every word that ends with “-ness”, is a noun. It is a noun that refers to a state of being in a specific kind of process. The process is certainly an action, but “consciousness” is referring to the state of being involved in the action, not the action itself of “being conscious” (the verb form). Consciousness is an active state.
Only if you are a solipsist. To sane people who believe in objective reality (that which is independent of one’s thoughts), value is merely a relative or subjective measure and space is an ontological element of objective reality that would exist even if there was never any consciousness anywhere.
Is that your issue? That reality doesn’t exist unless someone is conscious of it?
QM has no mysteries to it and QP is merely fantasy fysics. But what are you referring to when you say, “law of the observer”? Who made up that law?
…and feel free to address me as JSS.
I believe my topic, Complete List of All Functions is of use to you guys.
google.com/url?sa=t&rct=j&q … 4388,d.amc
JSS
I can concede to you that “abstraction” does NOT posses space. It does not change the validity of the idea. Numbers that are used in “physics” are numbers that represent things possessing space and value. Therefore the symbols or numbers, used should also represent both space and value. I also can agree with you that the universe can and does exist with out my consciousness or humans existing within it. But that is because I subjectively view a rock a conscious. Just not to our level. But I think that is another debate (What is the definition of consciousness) . The “Law of the Observer” states that consciousness collapses the wave function. The double-slit experiment is the idea I am reaching for here. An electron will exist as a particle if there is consciousness. Otherwise the electron behaves as a wave. Assumedly other particles. There are others that argue this idea as well. The “law of superposition”. If something that is in the state of superposition is observed, it will collapse into one positon. Also I am still on post approval, so I am replying as quickly as I can.
Thanks
Conway
Actually numbers represent the quantities of the things, not the things themselves.
The number “two” might refer to the quantity of 2 apples or 2 electrons or 2 laws of nature.
How much space does the number itself take up? Is that space between the apples or above them? Between the laws of nature or under them? Where and how much?
Consciousness is “Remote Recognition”. If something cannot remotely recognize, it is not conscious. The universe itself does not require that anything be able to remotely recognize anything. And rocks don’t possess the ability at all.
But that is not a law of nature. That is a law of mathematics. The wave function, merely an equation, is waiting for someone to fill in the variables so that it can be completed. Those variables cannot be filled in until one observes what is happening so as to gain the information. Once the variables are filled in, the equation becomes simplified, “collapses” into a simpler equation.
None of that has anything at all to do with physical reality. QM speaks merely of math models. A wave function is not a physical entity and nor does it occupy space other than the physical symbols being used to represent it.
Same as above. None of that has anything to do with physical reality. The physical electron doesn’t care what math model you are using to represent it. Your math model collapses. The physical electron does nothing any different than usual.
And the Young’s Double-Slit experiment is resolved by understanding harmonic resonance. The space in which the particles travel is not empty, but rather filled with waves that form a harmonic resonance (much like sound waves inside a speaker box). Particles get caught up in the harmonic wave pattern like a boat following waves on the ocean surface and thus end up striking the screen in a pattern just as boats would end up striking the beach in a similar pattern.
The only thing magical about it is that you cannot see those waves except by watching the effect they have on the particles.
You’re welcome.
JSS
By your definition of consciousness a computer is conscious. Does it not possess the ability to remotely recognize. Again in any case this is a different debate. I am aware of what CURRENT numbers represent. They represent as you said "quantities’ of things. It is an inherent truth however, that the most “accurate” symbols represent all “properties” of the thing it is symbolizing. I am glad you mentioned apples here. I shall give you a reasoning as to why I claim a number reprents both value, and space.
“It is possible to have 2 apples, it is possible to have 2 tiny apples, it is possible to have 2 large apples. In all cases I have the same number. But in no case do I have the same value”.
Further I think it would be wise to apply some real mathematics here. It is current mathematical fact that in the following equtions “one” of the numbers given does NOT really exists as a “number”.
2 X 3
This eqution means “literally”…
2 + 2 + 2
or it means
3 + 3
But you will note in one fashion the number 3 does not really exist. In the other it is the number 2 that does not really exist.
It is current mathematical fact that any time you multiply or divide…one symbol given is a value, one symbol is a space. Note this is NOT my theory, this is current fact.
Additionally I am aware that a wave function is a mathematical apparatus… it is used to describe waves…as you admit are real. It is then the unified field that the “wave function” represents. Something we can not easily define. But without a shadow of a doubt… is real…and it possesses space. As is my point with consiousnes possessing space. Again I have conceded to you that abstraction does not posses space (for the sake of argument). But if I am to be honest as a mathematician, philosopher, and a man, then I must use symbols that represent “all” the properties of the things it it intended to represent.
A yin yang with out the yang is insufficient and inaccurate.
That is true, although as you say, “not to our level” … although Samsung and Google are getting pretty close.
“CURRENT”??
That would be the most comprehensive, not the most “accurate”. All defined words/numbers are 100% accurate - “by definition”. Although some are a bit useless due to poorly worded or ambiguous definitions.
Again, a poor choice of word; “value”. Of course if you vary what it is that you have the quantity two of, then you have two of a different things, eg. “tiny apples” vs “large apples”. A tiny apple is not a large apple, just as an apple is not a orange nor a law of nature.
Well, that is not an “equation”, rather an “expression”, but okay those each represent an equivalent quantity/amount - three ways to say the same thing, much like having 3 sentences that express the same attitude toward a President.
One expression uses both a “2” and a “3” whereas the others only use one of the symbols, yes. That is like having 3 sentences wherein the word “love” and “hate” are used in one sentence and only “love” or “hate” is used in the other two.
And then also note that when the “2” is not used, the quantity is still presented by how many "3"s are presented. The number is merely the symbol for the quantity. If one has already represented the quantity properly, one need not present the symbol also.
Can you quote a source for that “fact” because it doesn’t make any sense to me. Each symbol represents a quantity whether multiplying, dividing, adding, or subtracting. The quantity of what is different for each case.
In Multiplying one quantity is the quantity/count of the other quantity - the number/quantity of sets (the other quantity).
In Dividing one quantity is the quantity/count of portions of the other quantity - the number of divisions of the other set.
In Adding and Subtracting both quantities represent the size of the sets of items (aka your “values”).
“Unified field”??
The wave function in QM represents a statistical probability graph, not a physical wave such as a radio or water wave. And even those “physical waves” are actually merely the physical shape of the substance, not the substance itself.
The shape that something is in does not take space itself. The shape is a description of the geometric distribution of the substance/item/“value” throughout space. The description itself does not take up space (not counting the mere symbols that might be used), else there would be less of the substance so as to leave room for the shape. Does a cube of clay take up more space than a sphere of the same amount of clay? Isn’t the amount determined by the disregard of its current shape?
Certainly the more comprehensive the words/numbers are regarding something, the better unless confusion is the intent (and often it is). But it is much like ensuring that all of the decimal places for Pi are represented each time one refers to Pi. Such things often can’t be done even when the extra inconvenience is allotted.
Only if one is referring to the entirety rather than only one portion, but yeah.
JSS
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So then if computers aren’t currently aware (agreed they are getting close), then the definition of consciousness provided by you is also lacking. (still a side issue)
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“current” numbers representing “labeling of quantities” as stated by you. I capitalized it to imply that it is a very old understanding. And that a number defined as a quantity of space and value is more accurate.
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I can agree with you here. My words were chosen poorly. “Comprehensive” being the better choice. So then do you agree?
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I can agree here as well. If not value…chose what word you like…the definition for value that was given should however remain the same. “Labeling of quantities of existence other than dimensions”. As given in the original post.
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Cut me some slack…I know an equation symbol is needed for an expression to be an equation…as you say you got the point anyway. As the sum is not the point in the debate…you will see I handled this with simply the variable X in the original post. That is… where as I was not implying a change in sums as currently understood.
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Ask any linguist. Ask any mathematician. The order of operations, and the “way” in which things are stated “can” make all the difference.
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The “fact” I mentioned is inherent. If the equation given is ( 2 x 3 = X ) …then it is that I write the (number 2) in ( 3 spaces ) and then add. Or it is that I write the ( number 3 ) in ( 2 spaces ) and add. This is how multiplication is understood. So clearly I have a number and a space. I put the number into the space’s and then add. One symbol is a value and one symbol is a space. That is the reality of this situation. That is the most “comprehension” definition for what the action of multiplication is.
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There are many different types of waves. There are many different types of “functions” representing’s these waves in mathematics. And it is that all waves are in reference to a probability spectrum. There is a specific “wave function” that “theoretically” represents the unified field. Of which particles collapse. Because of consciousness. Consciousness has space, the particle has space, the wave has space. In any case were getting off topic with QM. My point here was only for the purpose of supporting my argument for consciousness possessing space. As I have conceded to you this already. Additionally…I’m getting in over my head here in regards to QM. I can however link all references to laws I have mentioned.
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The consequences of this idea do not require an infinite amount of decimal labeling. The consequences of this idea allows for division by zero, reduces axioms, and reduces the number of number types, and as you agree more accurately describes numbers. Therefore it is a benefit not a pointless, and wastefull action such as the labeling the decimals of pi.
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It is impossible for you to refer to any portion of a whole, with out referring to the whole. I can not refer to yin, without subconsciously referring to myself and others, of yang. I can not talk of light with out mentioning dark. How do you explain to me what a positive charge is without explaining to me what a negative charge is. And so on. The symbol for any charge indicates inherently both bits of information. That is to say…"If I look up what the symbol for a “positive” charge means…it will define for me quite clearly the totality of information regarding positive and negative charges.
Not at all. Clearly consciousness comes in degrees as well as types (much like intelligence). Computers have a relatively low degree of consciousness and only of specific types. Homosapian is also limited to degree and type.
Well, I don’t see it as “more accurate” at all. And is actually a broken, incoherent ontology. I have yet to see how space has anything to do with numbers. You merely keep saying that it does.
I agree that we are most often better off when our words/numbers and sentences are more comprehensive. But that is not to betray coherence.
There are three concerns involved in Truth:
- Coherence and/or consistency
- Comprehensiveness
- Relevance
Any truth model, any ontology, must maintain all three of those at all times in order to be considered “true”. Relativity theory and quantum physics do not do so. They are each provably “not true” meaning that they cannot maintain coherency, comprehensiveness, and relevance. But note that quantum mechanics is not an ontological theory, but rather merely a tool for statistical measurements.
And to toot my own horn here for a short bit:
If you seriously want to see a unified field theory that is precisely true (as defined above), my own Rational Metaphysics: Affectance Ontology can’t be beat.
I can accept that a number (the symbol) is a “label of a quantity involving existence”, but why leave out dimensions? Each dimension has distance quantities involved; “2 meters”, “3 miles”, “31.5 degrees North by Northeast”…
As I expressed, I don’t see the relevance in pointing out that the same quantity can be represented in different ways. The same quantities were represented in each of your examples … “so what”? How were they related to numbers occupying space?
Of course the order of symbols changes the meaning of a sentence or expression. Again, how does that relate to numbers occupying space? The symbols for the quantities occupy space. But that isn’t what you have been talking about (EDIT: I didn’t think … until later in this post).
Emm… no. You are making the most popular conflation error of the day; “Confusing the map with the terrain”. Very common in quantum fairy tales.
The SYMBOLS occupy space. A quantity that a symbol refers to is NOT a physical thing, but a concept. The universe has no actual physical “two” in it anywhere. “Two” is a mental construct only and does not require space even though the brain thinking of it does. Mental construct, shapes, ideas, all require a physical device to represent them, but they are never actually physical themselves.
In QM all waves (and all things) reference a probability of one type or another. QM is nothing BUT probability analysis concerning the location of defined physical items. But then they forget to include the definition of the item and get carried away with the probability being the only (incomplete) description of reality.
As you pointed out, “yin-yang” requires both in order to be complete. Quantum physics (extrapolated from quantum mechanics) attempts to leave out the physical definitions and just go with the math probabilities of locations as if only locations and the math pointing to them existed. QP proposes that the mental graph is the ONLY physical reality when in fact, it is not physical at all.
Quantum Physics IS the conflation of the map with the terrain. It is technological age monkey talk. It is an incoherent and incomprehensive ontology, leaving out the physical items being represented so as to pretend that only the subjective mathematics exists and no objective reality at all.
One cannot believe in objective reality and also in quantum physics. They are not at all compatable, which is why you hear them say really dumb things about cats being alive and dead at the same time, observations changing physical reality, consciousness causing time reversal, and so on.
The Quantum Magi are VERY poor philosophers, assuming that they aren’t intentionally playing with the minds of the unsuspecting masses.
Ummm… I need to hear more details of that. I am not aware that QP has proclaimed a “unified field”. And again, this gets back to the wave function being proclaimed as the physical reality while double-talking that it merely represents physical reality. Either the wave function IS the physical reality (the “terrain”) or it is merely a representation/description of a physical reality (the “map”).
No. The math FUNCTION collapses. The particles couldn’t care less of anyone’s conscious state.
The brain that is conscious occupies space. The particles occupy space. And the wave is merely a description of the space being occupied, not occupying space of its own.
Well my concern has been that you keep proclaiming that concepts, such as consciousness and numbers “occupy space”. And as I have pointed out many ways, that simply cannot be “true” in the sense of being coherent and comprehensive.
Do you mean the consequences of the idea of concepts such as consciousness and numbers occupying space?
How does that “reduce” anything?
How does that allow for dividing by zero?
The issue with division by zero has been that the expression becomes insufficiently descript as “infinite”, but of no designated cardinality and thus cannot be used for much.
I still am not seeing how that issue relates to consciousness or numbers occupying space.
JSS
I yield any conversation in regards to QM. As I lack the education, and as I can not make a connection between Relative Mathematics and QM. I yield any conversation in regards to consciousness, as it is a separate debate. As to the following.
A = Any number other than zero
V = quantity of existence other than dimension
S = quantity of dimension
A(v) X 0(s) = A
0(s) X A(v) = A
but also the following is true
A(s) X 0(v) = 0
0(v) X A(s) = 0
Therefore in division
A(v) / 0(s) = A
0(v) / A(s) = 0
Division by zero.
It is a misnomer that division by zero is infinity. This is not the case. The sum of division by zero is “undefined”. You can argue that this does or does not have anything to do with infinite, but it is besides the point.
Further under Relative Mathematics, basic axioms such as…
Multiplicative property of zero
Multiplicative identity property of 1
Commutative property of multiplication
Are no longer necessary, therefore a reduction of axioms. Currently there are 7 different types of numbers. Under Relative Mathematics there is 4 kinds of numbers. Simplification. This also then shows that multiplication and division are RELATIVE to what symbol is representing space, and what symbol is representing value.
Such as space and time are measured relative to a body of reference, the sum of multiplication and division is relative to what is space and what is value. Relative Mathematics.
Okay, so let me see if I can put this into English:
So:
A symbol to represent a quantity(of a substance) * zero quantity (of a distance) = a symbol to represent a quantity.
You seem to be multiplying a symbol by zero distance. Multiplication requires that all terms be of the same type (apples or oranges, not a mix).
But even if we accept the zero as merely an amount, you are saying that you have zero symbol, not “A” which excluded zero.
And even if instead of A being merely a symbol, we accept it as an amount, we have a non-zero amount taken zero times and that is supposed to be a non-zero amount??
Something isn’t making sense. What am I misreading?
JSS
“A symbol to represent a quantity(of a substance) * zero quantity (of a distance) = A…a symbol to represent both substance and distance.”
In the act of multiplication the substance is “placed” into the distance. Thereby creating A, as a number, where A(v) or A(s) are only composites of A. Where as 0(v) and 0(s) are only composites of O.
For example…
2 substances placed into 3 spaces and then added
3 substances placed into 2 spaces and then added.
2 X 3
3 X 2
Where as the “distance” of zero and 1 are equivalent, Where as the “substance” of zero and 1 are not equivalent.
Okay, let’s try to move on…
You seem to be using terms that are not English.
A “substance placed into a distance” doesn’t seem coherent. One can place a substance AT a distance from some reference. But is that what you mean? Perhaps you mean to place a substance “at a location”?
And then how is a symbol (“A”) to represent a quantity of a substance created by placing a substance at/into a distance/location? Are you just talking about building the expression (eg “apple apple apple”)?
In English these sentences are not making sense.
So, put two apples in three places. And then count them ( = 6 apples).
Or, put three apples in two places and count them = 6 apples.
Where did that come from? And what does it have to do with anything?
JSS
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I was using the words that you chose. I prefer to say that a value is placed into a space…which makes a number.
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I stated clearly that a (substance/distance) was created when you place a (substance) into a (distance).
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Lastly I stated an actual field axiom in the orgianl post stating the commonaility of zero and one. And expressing this idea in one…albeit long sentence.
I have appreciated the depth of this conversation, if you tire of it, I understand and appreciate your time and efforts.
FIELD AXIOM
“For every A in S there exists a z1 and z2 compositing A, such that any A in operation of multiplication or division is only representing z1 or z2 in any given equation. Such that z1 for all A’s other than zero equal A. Such that z2 for all A’s other than zero equal A. Such that z1 for zero equals zero, such that z2 for zero equals one.”
I’m afraid that I can’t follow your use of language well enough to decipher what you are fundamentally trying to say, much less by what rationale you propose to support it.
There is a serious flaw in your argument, conway.
You first define an object as “It is the inherent nature of all things that they are a compilation of two different and distinct things. It is axiomatic that these two things are space and value. The value of any given thing being what it is, while the space is what it occupies.”
So, you define “space” as “that which the object is not” then you define space as a second, alternate definition “the position in which it occupies.”
THroughough your whole thesis it is cluttered…you mention “space” as the position in which something occupies, even though you gave it the definition of “that which it is not.”
I recommend rewriting your whole thesis, changing the word “space” to “position” in all relevant instances.