1 + 1 = 1
1 + 1 = 1
I'm reading an interesting book about equations. And the author states that the simplest we talk about in everyday life, like when we were kids, is 1 + 1 = 2. And he then relates this to experience: I have an apple, you have an apple. We toss them into a bucket and together we have two apples. Point being that equations, and math in general is so useful because it relates to the real world.
That all makes sense until I think of this: I have a drop of water in my hand. You have a drop of water in your hand. We both dump our drops into a cup and what do we get? One drop of water. The volume is double, but the count itself is 1.
Or let's say I smash 1 rock into another rock, and the result is a bunch of rocks. Cleary 1 + 1 = more than 2.
My point is, even the simplest of mathematical equations only correspond to "reality" if and only if we selectively choose our examples.
Thoughts?
That all makes sense until I think of this: I have a drop of water in my hand. You have a drop of water in your hand. We both dump our drops into a cup and what do we get? One drop of water. The volume is double, but the count itself is 1.
Or let's say I smash 1 rock into another rock, and the result is a bunch of rocks. Cleary 1 + 1 = more than 2.
My point is, even the simplest of mathematical equations only correspond to "reality" if and only if we selectively choose our examples.
Thoughts?
Re: 1 + 1 = 1
Already address a portion, but not all of the this argument already.RustyBert wrote: ↑Wed Dec 13, 2017 7:30 pm I'm reading an interesting book about equations. And the author states that the simplest we talk about in everyday life, like when we were kids, is 1 + 1 = 2. And he then relates this to experience: I have an apple, you have an apple. We toss them into a bucket and together we have two apples. Point being that equations, and math in general is so useful because it relates to the real world.
That all makes sense until I think of this: I have a drop of water in my hand. You have a drop of water in your hand. We both dump our drops into a cup and what do we get? One drop of water. The volume is double, but the count itself is 1.
Drops are volumes in themselves, so I do not necessarily agree with you example, however I get the point you are trying to make and their is a lot of substance to it.
Or let's say I smash 1 rock into another rock, and the result is a bunch of rocks. Cleary 1 + 1 = more than 2.
That is an act of fractation, or "fractions" as "division".
My point is, even the simplest of mathematical equations only correspond to "reality" if and only if we selectively choose our examples.
Or do the examples reflect the right equations? Like I said before, I do not necessarily agree with your examples, however I agree with the point you are trying to make. With quantum mechanics being the forefront foundational "science" of our technological civilization, math might have to be updated a little considering the nature of dimensionality. Dimensions are merely measurements in themselves that produce further measurements. In these respects, what we understand of the standard arithmetic as producing one value is strictly a relativistic measurement that does not take into account further potential dimensions that exist as a result.
Thoughts?
viewtopic.php?f=26&t=23228
Take for example the equation that provides the foundations of “1” (1 ≡ 1 ≅ 2,1,2):
One reflecting upon itself is congruent in structure to .2,1,2
(1 ≡ 1) ≅ 2,1,2
***** (2,1,2 = < = “angle”)
One reflecting itself intradimensionally maintains itself as both stable (never changing) and unified. This act of SelfReflection or Mirroring is equivalent to One as Point directing itself into itself. The point is observed as both unified and stable in 1 intradimensional nature.
This is the first degree function:
a) 1 ≡ 1 → 1 ∵ (1 ≡ 1) = (⦁ = 1)
Simultaneously this act of intradimensional reflection manifests "2" because 1 reflecting 1 is structurally congruent to 2. 2 exists perpetually as 1 reflecting upon 1 and in this respect, exists at the same time in a different respect to 1. As one is always mirroring itself, 2 is ever present as a structural extension of 1.
This is the second degree function:
b) 1 ≡ 1 → 2 ∵ 1 ≡ 1 ≅ 2
One mirroring itself takes a dual role of reflecting itself as both 1 and 2. In these respects 1 and 2 manifest as approximates of each other through (1 ≡ 1). As approximate points they form 1 dimensional lines to connect them. 1 point would form two corresponding negative dimensional lines to 2 as 2 (or 2 ≈ 3 → 6, 3 ≈ 4 → 12, etc.). In these respects approximation as individuation through the 1 dimensional line can be observed as a multiplication function resulting in negative numbers when confined to positive values.
This is the third degree function:
c) 1 ≡ 1 → 2 ∵ 1 ≡ 1 → 1 ≈ 2
Thus the first shape formed is the angle: (2,1,2 = < = “angle”)
As all number is composed upon a selfreflecting one, all 1n follows the same form and function.
Re: 1 + 1 = 1
This opens up a brand new branch of mathematics.
1 + 1 = 1
This means that
1 = 1 + 1
Which means that
n = 1 where n is any positive integer, because
n = 1 + 1 + 1 + 1... + 1 ... +1
any sum of two ones is equal to one, so you just keep grouping the series into components (1+1) and then reducing each group to 1, and forming new groups, also then reducing them, finally ending up with 1.
This has great uses in the real world.
We just have to go out and find what these uses are.
It's never math's fault. The fault's our inability to realize that this is a great math tool, once we find the proper application for it.
1 + 1 = 1
This means that
1 = 1 + 1
Which means that
n = 1 where n is any positive integer, because
n = 1 + 1 + 1 + 1... + 1 ... +1
any sum of two ones is equal to one, so you just keep grouping the series into components (1+1) and then reducing each group to 1, and forming new groups, also then reducing them, finally ending up with 1.
This has great uses in the real world.
We just have to go out and find what these uses are.
It's never math's fault. The fault's our inability to realize that this is a great math tool, once we find the proper application for it.
Re: 1 + 1 = 1
Indeed.
Indeed, the concept has existed in man's mind so long, that people speaking the English language have incorporated into its system the way it treats quantities that are countable (like drops of water) differently from how it treats quantities that are not counted (water).
Much water  many drops of water.
Little water  few drops of water.
More water  more drops of water.
Less water  fewer drops of water.
Largest amount of water  most drops of water.
Least amount of water  fewest drops of water.
Notice how the third case is not different for the two different types of quantities. There is an argument to be said for using "manier drops of water" but that is not English. And some use the form "Much more many drops of water", to preserve the distinction between countable and notcountable qualities in the form of the expression.
And notice in your everyday walkabouts that people incorrectly use "less" for many things: "there were less people at the mall today", whereas the correct form would be "there were fewer people at the mall today". People these day say, "less days are cold in the winter", "less bicycles are on the road", "less would have been more", whereas the word they ought to use is "fewer" instead of less. In the last sentence, the topic of conversation being how many times people use the word "less".
But in these following instances "less" is correct:
 less fresh water is available for the poor nations of the world
 the rich are eating less
 a lot of people are getting less and less rich
 ..., lest Les lets lots less lust loose.  this is a partial sentence, used as a warning that in the (unquoted) first part something has to be done, in order to avoid Les to curtail gratification of his sexual desire by a great amount.
Then again, it's also always useful to reinvent the wheel, by pointing out that there are quantities that are counted, and quantities that can't be counted, for it is better to invent a wheel many times than nonce at all.
Re: 1 + 1 = 1
One potential degree of what the argument observes is that all acts of measurement act as "units" in themselves and our application of measurement is an application of 1.
Even in the observation of sets, the set itself is still "1" measurement. In these respects what we observe, as measurement is an act of unification and individuation into units through 1. In these respects what we understand of 1 is a universal dimension of measurement itself which gives boundaries as form.
1, in these respects, is the boundary of measurement as dimension, with dimension equivocating to space as direction.
We can observe this within the dimensions that form geometric figures as 1 moving and mirroring (stabilizing) forms through the line. In these respects that application of measurement is the application of dimension as 1 structuring itself adinfinitum through a mirror process.
"1 + 1 = 1" while not correct in its presention, is still an observation of the nature of 1 mirroring itself. In these respects the nature of number contains a "mirror" effect inherent within it. We can observe this in the process of measurement itself as forming dimensions that act as limits which both "unify" the structure as "1" and in a dual perspective "individuate" it constantly as "units". This form of individuation, as seperation, can be observed in the golden ratio as a continuous fraction:
1+1/(1+1/(1+1/(1+1/(1+1/(1+⋯)))))
As a dimensional limit, 1 may be viewed as synonymous with proportionality, with all dimensional limits forming proportions in themselves. 1 in these respect can be observed as synonymous with the 1D line as a spatial element. We observe this intuitively with 1 oftentimes equateing to the line, or some approximate of it, in various cultures.
While I don't necessarily agree with the examples given, the intuitive premise of the argument is correct and it may comfortably be implies that 1 is synonymous to a dimension in itself.
Even in the observation of sets, the set itself is still "1" measurement. In these respects what we observe, as measurement is an act of unification and individuation into units through 1. In these respects what we understand of 1 is a universal dimension of measurement itself which gives boundaries as form.
1, in these respects, is the boundary of measurement as dimension, with dimension equivocating to space as direction.
We can observe this within the dimensions that form geometric figures as 1 moving and mirroring (stabilizing) forms through the line. In these respects that application of measurement is the application of dimension as 1 structuring itself adinfinitum through a mirror process.
"1 + 1 = 1" while not correct in its presention, is still an observation of the nature of 1 mirroring itself. In these respects the nature of number contains a "mirror" effect inherent within it. We can observe this in the process of measurement itself as forming dimensions that act as limits which both "unify" the structure as "1" and in a dual perspective "individuate" it constantly as "units". This form of individuation, as seperation, can be observed in the golden ratio as a continuous fraction:
1+1/(1+1/(1+1/(1+1/(1+1/(1+⋯)))))
As a dimensional limit, 1 may be viewed as synonymous with proportionality, with all dimensional limits forming proportions in themselves. 1 in these respect can be observed as synonymous with the 1D line as a spatial element. We observe this intuitively with 1 oftentimes equateing to the line, or some approximate of it, in various cultures.
While I don't necessarily agree with the examples given, the intuitive premise of the argument is correct and it may comfortably be implies that 1 is synonymous to a dimension in itself.
Re: 1 + 1 = 1
Interesting discussion so far. The thing I've been considering is advanced math used in Physics. I don't pretend to know what they're talking about. But they do seem to be using equations fast and loose, as if the equations themselves had some independent reality. So when I think about an equation as simple as in my OP, even that really only has meaning in a specific context and is dead wrong depending on the context. So how can the advanced equations be any better?
Re: 1 + 1 = 1
RustyBert wrote: ↑Thu Dec 14, 2017 7:45 pm Interesting discussion so far. The thing I've been considering is advanced math used in Physics. I don't pretend to know what they're talking about.
Ask any honest physicist and he will tell you in the advent of quantum mechanics they feel the same way. The problem of physics, from what I am reading, appears to be one of categorization as measurement. The axioms we use for measurement in turn provide the structures we observe. Assuming this to be the case, even at the partial level, then the nature of the axiom as measurement must be measured itself. We can observe this simply as the application of one.
Further more, we can observe that 1 as measurement provides the foundations of measurement we see in number theory as arithmetic. A positive 1 reflecting a positive 1 is addition. A positive 1 reflecting a negative 1 as subtraction. Addition reflecting itself as multiplication, subtraction reflecting itself as division, multiplication reflecting itself as exponentiation and division reflecting itself as root appears by all accounts as 1 relfecting itself through three dualistic degrees of selfreflection.
If this is the case then all number, as extensions of 1, can be observed as a "mirror space" which provides the foundations for symmetry which in turn provides the foundation for structure...then being...etc.
But they do seem to be using equations fast and loose, as if the equations themselves had some independent reality. So when I think about an equation as simple as in my OP, even that really only has meaning in a specific context and is dead wrong depending on the context. So how can the advanced equations be any better?
The equations they used are strictly quantitative in nature, and for them to hold any resemblance to reality they must simultaneously reflect a qualitative nature. In these respects number theory must advance an understand of number as qualitative in nature. If we observe quality, strictly as dimension, this may provide some foundation considering dimensions are "space as direction".
Mathematics has ironically become assymetrical considering it focuses on quantitative degrees alone. A qualitative understanding would help. If you look at some the equations in quantum mechanics a significant proportion can be observed as divided or rooted through "2". 2 implies some degree of polarity as directions which are directed into or away from eachother. In these respects we are bound to get answers which continually flux as the axioms we use are conducive to them. Viewing 2 as polar in nature implies 2 as a source of continual flux.
Re: 1 + 1 = 1
What we understand of contradiction is primarily a deficiency in structure of an axiom. We observe something and this observation is not proportional in one degree or another.
Take for example the simple math problem 2 + 2 = 5
By all accounts this qualifies as a contradiction. The problem occurs with what forms the contradiction itself. "2", "+", "2", "=" and "5" are all axioms in themselves and true on their own account. The structuring of these axioms results in a disproportionality that inherently leads to a deficiency in "structure".
In this respect all contradictions fundamentally are a deficiency in structure and not a thing in themselves. This deficiency in structure can be purely:
1) subjective (as a person claims it is contradictory because it is not proportional to the axioms they observe)
2) objective (2 + 2 will always equal 4 therefore it cannot equal 5)
As all contradiction is strictly deficiency in axiomatic structure, the nature of contradiction is neutralized through structural propagation.
The continual propagation of structure, which may appear random, does not imply contradiction. Structures which may appear contradictory, such as 2 + 2 = 5, may not always contradict if they continually reflect through an observer as a unifying median. To further this example:
2 + 2 = 5
→
2 + 2 ≠ 5
→
2z + 2z = 5 ↔ z = 1.25
→
2x + 2y = 5 ↔ {x = 1...0 y = 1.5…2.5} ∨ { x = 1.5…2.5 y = 1...0} with x≜y
→
ad infinitum; therefore:
2 + 2 = 5 ↔ (2 + 2 = 5) = □
In this respect all axioms maintain a degree of contradiction where they lack symmetry or balance. However observing the contradiction as a contradiction is a simultaneously solution.
In this respect all axioms maintain a duality of truth and falsity as contradiction exists where definition is deficient.
Take for example the simple math problem 2 + 2 = 5
By all accounts this qualifies as a contradiction. The problem occurs with what forms the contradiction itself. "2", "+", "2", "=" and "5" are all axioms in themselves and true on their own account. The structuring of these axioms results in a disproportionality that inherently leads to a deficiency in "structure".
In this respect all contradictions fundamentally are a deficiency in structure and not a thing in themselves. This deficiency in structure can be purely:
1) subjective (as a person claims it is contradictory because it is not proportional to the axioms they observe)
2) objective (2 + 2 will always equal 4 therefore it cannot equal 5)
As all contradiction is strictly deficiency in axiomatic structure, the nature of contradiction is neutralized through structural propagation.
The continual propagation of structure, which may appear random, does not imply contradiction. Structures which may appear contradictory, such as 2 + 2 = 5, may not always contradict if they continually reflect through an observer as a unifying median. To further this example:
2 + 2 = 5
→
2 + 2 ≠ 5
→
2z + 2z = 5 ↔ z = 1.25
→
2x + 2y = 5 ↔ {x = 1...0 y = 1.5…2.5} ∨ { x = 1.5…2.5 y = 1...0} with x≜y
→
ad infinitum; therefore:
2 + 2 = 5 ↔ (2 + 2 = 5) = □
In this respect all axioms maintain a degree of contradiction where they lack symmetry or balance. However observing the contradiction as a contradiction is a simultaneously solution.
In this respect all axioms maintain a duality of truth and falsity as contradiction exists where definition is deficient.

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Re: 1 + 1 = 1
if water doesn't drop in zero gravity, how can you do math in space?
Imp
Imp
Re: 1 + 1 = 1
It divides/multiplies according to its relations, ie object hitting it.Impenitent wrote: ↑Wed Dec 27, 2017 11:19 pm if water doesn't drop in zero gravity, how can you do math in space?
Imp

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Re: 1 + 1 = 1
Interesting, this is kinda like changing the assumption that 100/4 = 25. It could just as easily be "modified" or "changed' to 33+33+33+1= 100. If that makes sense. A sort of unequal division.
Re: 1 + 1 = 1
Each number is "1" in itself, and as far as I understand it does not contradict set theory. As far as I understand 100/4 is about 4 being equal to 4 as proportions. Each proportion is equal in 4 seperate yet equal dimensions.Plato's Rock wrote: ↑Thu Dec 28, 2017 2:57 am Interesting, this is kinda like changing the assumption that 100/4 = 25. It could just as easily be "modified" or "changed' to 33+33+33+1= 100. If that makes sense. A sort of unequal division.
The act of division is the act of measurement through the application of dimensions as divisors. In these respects, division maintains a trifold nature of 1 in 3 as (x,y,z) which we can observed further in another trifold nature as multiplication being proportion to (division proportional to division):
(x*y = z) ∝ ((z/y = x) ∝ (z/x = y))
What we understand of division merely extends from 1 as a negative nature. Considering division is strictly subtraction reflecting subtraction, and 1 reflecting "x" is merely one as subtraction, negative one reflecting negative 1 results in:
2 as substraction
/2 as division (while still being negative as 2)
1 as subtraction
/1 as division.
In these respects we can observe division as having an inherent dualist nature that stems through "1" as the dimensional limit manifesting the equation. In these respects division is merely one individuating itself into further "1"'s as extension of 1.
Like I said before 1 + 1 ≠ 1 however the intention of the argument is correct.
However if observed as numbers mirroring ("≡" = mirror, "≅" mirror equivalent, "≈" = approximate to) :
(1 ≡ 1) ≅ (2,1,2)
(2,1,2)= “angle”
One reflecting itself intradimensionally maintains itself as both stable (never changing) and unified. This act of SelfReflection or Mirroring is equivalent to One as Point directing itself into itself. All number inherent within this first degree function manifests as part of the values produced. The point is observed as both unified and stable in 1 intradimensional nature.
This is the first degree function:
(1 ≡ 1) → 1
Simultaneously this act of intradimensional reflection manifests "2" because 1 reflecting 1 is structurally congruent to 2. 2 exists perpetually as 1 reflecting upon 1 and in this respect, exists at the same time in a different respect to 1. As one is always mirroring itself, 2 is ever present as a structural extension of 1.
This is the second degree function:
(1 ≡ 1) → 2
One mirroring itself takes a dual role of reflecting itself as both 1 and 2. In these respects 1 and 2 manifest as approximates of each other through (1 ≡ 1). As approximate points they form 1D lines to connect them. 1 point would form two corresponding negative dimensional lines to 2 as 2 or
(x ≈ y ) → z
In these respects approximation as individuation through the 1D line which can be observed as a multiplication function resulting in negative numbers when confined to positive values. Through M.D.R arithmetic approximation is considered a function.
This is the third degree function:
(1 ≈ 2 ) → 2