Create or die (a 3 months mission)

[Guest Doron Shadmi]

The goal of this thread is to find a logical reasoning system, which can be used as a common basis for both our morality development and our technological developments.

 

If we achieve this goal, then I think that we improve our chances to survive the power of our technology.

 

==========================================================================

 

If we look at Drake's equation http://www.setileague.org/general/drake.htm we can find parameter L.

 

L = The "lifetime" of communicating civilizations, or in other worlds, if there is no natural catastrophe in some given planet, then how some civilization survives the power of its own technology?

 

If we look on our civilization, I think that we cannot ignore L and in this case we should ask every day "how we survive the power of our technology?"

 

My work for the last 20 years is one of many possible ways to answer this every day question.

 

Though my research I have found that if some civilization has no balance between its morality level and its technological level, then there is a very high probability that its L= some n , or in other words it is no longer exists.

 

Now, let us look at our L and let us ask ourselves: "Do we do all what we have to do in order to avoid some n?"

 

Most of the power of our technology is based on the Language of Mathematics and its reasoning, where the current reasoning is generally based on 0_XOR_1 logical reasoning, and there is nothing in this reasoning which researches the most important question which is: "How do we use this powerful Language in order to find the balance between our morality level and our technological level"?

 

If our answer is: "The Language of Mathematics has nothing to do with these kinds of questions", then in my opinion we quickly bring ourselves to find the exact n of our L.

 

In my opinion, in order to avoid the final n of our L, we have no choice but to find the balance between our morality level and our technological level within the framework of what is called the Language of Mathematics.

 

Furthermore, we should not leave this question to be answered beyond the framework of our scientific methods, because no other framework, accept our scientific method can really determinate the destiny of our L.

 

==========================================================================

 

THE GAME FOR OUR LIFE

 

Let us say that we are members of a team that have exactly 3 months to live, unless we create a useful pure mathematical system.

 

For this mission we have no choice but to define these independent concepts:

 

1) Emptiness (notated by {})

 

2) Fullness (notated by {__})

 

3) A point (notated by {.}}

 

4) A segment or interval (notated by {._.}

 

Some initial terms:

 

$Tautology:

The identity of a thing to itself.

 

(It means that in this framework we do not need 'if, then' proposition in order to define the self existence of some element, which means A=A holds without using ‘if, then’ proposition)

 

$Set:

A $set is a collection of objects in which order has no significance, and multiplicity is also ignored.

 

$Multiset:

A $set-like object in which order is ignored, but multiplicity is explicitly significant.

 

$Singleton $set:

A $set having exactly one element a. A $singleton $set is denoted by {a}, which is an example of a collction of exactly one element.

 

$Urelement:(no internal parts)

An $urelement contains no elements, belongs to some $set, and it is not identical to a $set that has no collection of elements in it.

 

‘=’ notation is used for both $tautology (4=4) and quantity equality (4=2+2), which means that this system has to distinguish between elements not only by their quantity and/or order, but also by their structural properties, for example:

 

0 = .

 

1 = 0_1

 

2 = 0__2

 

3 = 0___3

 

4 = 0____4

 

are all $tautologies, where 4 = 3+1 (for example) is not a $tautology but quantity equality between the two different structures {0____4} and {0___3, 0_1}.

 

Also any arbitrary segment can be considered as 1, and in this case the rest segments heve their unique notations according to this segment.

 

Please give your ideas that can help us to survive this mission, thank you.

 

(All I have to say in this thread can be found only in the opening post, so any dialog with me will be only about the initial conditions, and how to correct them, if you think that they need to be tuned.

 

It means that I leave the stage for other persons who wish to develop a system from these initial conditions, thank you)

 

These are only initial conditions, so do what you think is needed to do in order to develop a useful system.

 

But please do that without ignoring any of the initial conditions.

 

==========================================================================

 

The nature of this thread (Topic)

 

The nature of this thread needs more time to develop a meaningful posts because it gives an opportunity to each participator in it to show how he uses its own abilities to survive an unfamiliar situation, which is basically different from what he have learned in the standard academic system.

 

1) You have to define the initial conditions by yourself (by using your own abilities to survive after 3 months).

 

2) In order to do that, you have no choice but to look at this situation from a new point of view, which is not the standard logical reasoning of 0_XOR_1, which stands in the basis the standard academic system.

[MandrakeRoot]

I dont quite understand what you want to do, but it looks like you are trying to reinvent some parts of set theory here.

In set theory the so called finite cardinals can be identified with the natural numbers, but they are also sets :

 

e.g., 0 = emptyset

1 = {emptyset}

2 = {emptyset,{emptyset}}

so 0 is an element of 1 which is an element of 2 etc...

(allowing you to create an order, a <= b iff a element of b)

 

Mandrake

[Guest Doron Shadmi]

Hi MandrakeRoot,

 

Can you define rigorous definitions to a), b), c), d) in post #1 ?

[MandrakeRoot]

Well you will need an axiom to define the emptyset. Basically something like "there is a set such that every element is not in it". So then you have what you call emptyness.

 

I am not sure what you mean with fullness though ?

 

A point is a synonym for element (of a set) i would say.

 

With the axioms of set theory you can create the natural numbers, once you have these you can create and define perfectly all other numbers and prove statements such as "in between any two rational numbers there is an irrational number" (also in between any two irrational numbers there is a rational number).

An interval is just a set : the notation [a,b] is just short hand for the expression :

[math] [a,b] := \{x \in \mathbb{R} \; : a \leq x \leq b\}[/math],

 

Does that answer your question ?

 

Mandrake

[Guest Doron Shadmi]

Please pay attention to the blue word:

 

For this mission we have no choice but to define these independent concepts:

 

a) Emptiness (notated by {})

 

b) Fullness (notated by {__})

 

c) A point (notated by {.}}

 

d) A segment or interval (notated by {._.})

[e(ho0n3]

Emptiness and fullness are intricately tied to one another, i.e. you can't define one without knowledge of the other and vice versa. It's like trying to define "true" without "false" and vice versa.

[Guest Doron Shadmi]

Hi e(ho0n3,

 

What you say holds only from 0_XOR_1 point of view.

 

In this case you have no choice but to look at post #1 by using a different logical reasoning.

[fuhrerkeebs]

Congratulations! Your one the millions of people who think they've done something inventive. Too bad your about hundred years too late...everything you've stated is pretty much basic set theory...if it's not, let me know how it isn't.

[e(ho0n3]

Hi e(ho0n3' date='

 

What you say holds only from 0_XOR_1 point of view.

 

In this case you have no choice but to look at post #1 by using a different logical reasoning.[/quote']

Do you want me reason from the XNOR point of view? This is starting to remind me of intuitionistic set theory, which is full of strange, albeit interesting, notions. Have you ever looked into this kind of set theory before? I think it may be up your alley.

[MandrakeRoot]

Probably in any reasoning format fullness and emptyness would be related. So the concepts you are trying to define will be dependant in any situation.

Why trying to reason in another format that current mathematical reasoning ?

This reasoning would work excellent in society also i guess.

 

Can you explain better why our society would die out if we continue to reason using mathematical reasoning ?

 

Mandrake

[Guest Doron Shadmi]

Please read some part of my dialog is another forum, on this subject:

 

that new scientific discoveries may lead to better means

When I am talking about scientific discoveries' date=' I am not talking only about new physical quantified phenomena and technological methods to use it.

 

I am also talking about the education process that will be an inherent part of the scientific framework, which takes in account the power of the language itself on the human mind and discover by using this power the most intimate and internal levels of the power of constructive life within each one of us.

 

This is the supreme responsibility of the scientific method, to use its power to support and save life phenomena, by using the best methods that can be found and developed by us.

 

Again, there is no Math without Mathematicians, there is no science without scientists, and there is no life without leaving creatures, simple as that.

 

We have no choice but to do the best we can in order to save and support life on this planet, because in this case, after we got the power to destroy ourselves, we cannot speak anymore on arrows or knives, because arrows or knives or not going to destroy most or all of us not today and not tomorrow.

 

We are no longer waking on a sidewalk but on a tight rope high above ground, and we have to use our best methods to not falling from this rope.

 

And more power means higher and thinner rope that we have to deal with, if we want to survive the blind power of our discoveries.

 

In short any powerful method always have its destructive and constructive sides, and we have no choices but to do the best we can in order to use it with open eyes, and nobody but us is responsible for this.

 

whole-heartedly agree. Matt grime, HallsOfIvy, Hurkyl, and others have already gone around and around in circles with Lama on the mathematical front.

You cause yourself not to understand my work by looking on the Language of Mathematics only from the point of view of its powerful technical abilities which are based on the 0_XOR_1 reasoning, and this reasoning does the best it can to clearly and sharply separate its methods from any philosophical, moral or ethical researches.

 

Furthermore, the mathematicians congenital abilities are not taken as natural parts of 0_XOR_1 reasoning.

 

And the reason is very simple, 0_XOR_1 is an artificial reasoning that has nothing to do with real abstract or non-abstract HIGHLY complex systems.

 

On the contrary the included-middle reasoning is the right logical reasoning that can support both our technological and non-technological abstract or non-abstract aspects of life.

 

And why is that?

 

Because it is based on the most problematic situation that can exist, which is: To find how opposites interact at least without destroying each other and at most to develop higher and deeper levels of interactions between HIGHLY complex phenomena.

 

A person does not change their basic nature via the acquisition of more knowledge...

 

Or can they?

If we are using ! sign right from the beginning about this subject, then we are with our own hands fixed our destiny about this subject.

 

So I think that your "or can they?" question is the right answer to any defeatist attitude about this subject.

[fuhrerkeebs]

Again, there is no Math without Mathematicians, there is no science without scientists, and there is no life without leaving creatures, simple as that.

 

Let me tell you something...my 6 year old brother can do math, science works regardless of whether we understand it, and that last sentence is such an amazingly genius tautology that there is no disputing it!

 

And guess what buddy? I see nothing about your math to distinguish it from classical logic and set theory.

[Guest Doron Shadmi]

Then dear fuhrerkeebs, you don't know what is included-middle reasoning, which is definitely not the logical reasoning that standing in the basis of ZF.

 

If you want some hint then press on my website address, at the bottom of this post.

[fuhrerkeebs]

Your included and excluded middle logic does make some sense, but you don't even know how to use it right. You say the dual nature of the photon is included-middle, because the wave nature and the particle nature of the photon prevent/define each other, when they don't. They actually prevent each other and define the photon.

[e(ho0n3]

Then dear fuhrerkeebs, you don't know what is included-middle reasoning, which is definitely not the logical reasoning that standing in the basis of ZF.

What about ZF? There are other set theories which have included-middle axioms, particularly those based on intuitionistic set theory. I know of a set theory called IKP which maybe just what you're looking for. The journal of symoblic logic is a good source for these sort of things. Have you ever tried publishing your ideas formally?

[MandrakeRoot]

I still dont see why 0 1 reasoning will lead to destruction of the world. We are seriously polluting the world because we are stupid and not because we reason 0,1.

This is by the way a very natural reasoning methinks, and doenst exclude any moral reasoning at all.

 

Like e(... says you are probably just looking for another set theory.

 

Mandrake

[Guest Doron Shadmi]

...because the wave nature and the particle nature of the photon... prevent/define each other...

I wrote prevent/define their middle domain, which is the photon.

 

If I wrote by mistake "each other", then I'll find it and correct it to: "their middle domain".

 

Because in my included-middle system two opposited are independent.

[Guest Doron Shadmi]

There are other set theories which have included-middle axioms...

Thank you for the information about IKP.

 

As much as I now, no one of these set theories, includes our own cognition to define the number concept, and then to use this cognition/element(s) interactions as a gateway between our moral side to our reason_formal_technical side, under a one organic framework, that uses the deep ability of included-middle reasoning to interact between independent opposites in non-destructive ways.

[Guest Doron Shadmi]

I still don’t see why 0 1 reasoning will lead to destruction of the world. We are seriously polluting the world because we are stupid and not because we reason 0' date='1.

This is by the way a very natural reasoning methinks, and doesn’t exclude any moral reasoning at all.

 

Like e(... says you are probably just looking for another set theory.

 

Mandrake

[/quote']

This dichotomy between our morality and our logical reasoning is a new method that was created 500 years ago mostly by Rene Descrates (1596-1650) and Francis Bacon (1561-1626)http://trumpeter.athabascau.ca/content/v10.3/Jung.html.

 

And I am not talking about the biblical morality model, but on the idea of "power over nature" that standing in the basis of Descrates' and Bacon's philosiphy.

 

This point of view is the basis our modern technological civilization, that still directed by this "power over nature" idea, which can quickly lead us to a dead-end street of the history of life on this planet.

 

Morality, In my opinion, is first of all our basic reasoning of natural balance with the fragile and complex phenomena of life on this planet, which we are part of it (whether we like it or not) and not "power over nature" of it.

 

The most "dangerous zone" of this "power over nature" idea can be found in the logical reasoning that standing in the basis of formal and platonic school of thought, where humanity and nature’s non-trivial complexity has no room.

 

Instead of humanity and nature’s non-trivial complexity, Formalism and Platonism are based on scholastic and artificial methods that look at logic as some scholastic game (in the case of formalism) or a universal principle, which is out of this world (in the case of Platonism).

 

So as you see "power over nature" has many faces in our modern civilization,

and this imbalance can lead us like a pendulum movements, to the opposite side of irrationality which is based on superstitious and some primitive aspects of fundamentalist beliefs.

 

This cocktail of mass destruction weapon and primitive fundamentalist beliefs, are both based on the same "power over nature" idea.

 

My project is to construct a new Language of Mathematics, which is based on the "balance with nature" which is, in my opinion, the most meaningful logical reasoning of any living thing in this universe.

 

 

Someone in another forum gave game theory as an example of how Mathematics can be a gateway that help us to survive conflicts by analyze the reasoning that stand behind them and he quoted Stanford university website, where we can find this sentence:

 

"Game theory is the study of the ways in which strategic interactions among rational players..."

 

In my previous post I said that this theory cannot fully answer to this question if:

 

1) It does nothing to show what it means by using the words 'rational player', because it takes 0_XOR_1 logical reasoning as the one and only one meaning for the words 'rational player'.

 

2) There is one and only one real meaning to the word 'strategic', which is: "How we avoid n of L in Drake's equation http://www.setileague.org/general/drake.htm ?" (as clearly explained in post #1)

 

I suggest anyone of you to open, for example, Google and search for:

 

"Drake's equation" + "game theory"

 

And you will see by yourself the "strategic big efforts" of the human race to give its solution to L of Drake's equation.

 

Nothing, but our morality level, can prevent from us to build an atomic weapon.

 

What I am suggesting will not prevent from us to discover any new powerful thing.

 

The deep change that I am talking about is to use this powerful language of mathematics in such a way that any new student who learn it will use a built in methods that develop both his morality level and his technical skills in such a way that will give him the strategic insight not to use his power to develop destructive things from one hand , and to take care about life on the other hand.

 

Look how we separate so easily between what is called science methods and morality.

 

And this is exactly what the academic system sells to young students and they buy it.

 

So let me say it again, because of this artificial separation between our morality and out scientific methods that are learned by the academic system for the last 200 years, our world got all its mass destructive weapon.

 

The logical reasoning that I am talking about it is the included-middle reasoning, which is based on our abilities to develop deep interactions between abstract or non-abstract elements in such ways that they will not destroy each other during their interactions.

 

This kind of reasoning, when combined with our own cognition abilities to develop Math as part of the research itself, can lead us to develop a new kind of language of Mathematics which is deeply connected to our morality level.

 

And I am not talking about avoiding knowledge from increasing.

 

On the contrary, I am talking about developing better methods which will give us the abilities to deal with the power of our discoveries and the knowledge that we get from these discoveries, in such a way that will save us from the blind forces of our discoveries.

 

Our morality first will save us from the blind forces which existing within us, and can be seen from time to time during our wars.

 

And the next global war will be our last war.

 

So this is the time to take the technologies which we developed during the wars between us, and put our efforts in order to develop technologies that will save our planet from KT asteroids, for example.

 

Our morality level is our only guaranty to survive power that can be discovered by us in the future, and this morality level has to be developed all the time if we want to survive these discoveries.

 

This is a very long story if we keep continue to develop our morality, and it can be easily a short story if our morality level is neglected by us during our technological development.

 

No single method can eliminate the possibility of thoughts of mass murder, it only can reduce its chances to become our reality.

 

If each person in this planet has a deep understanding which is based on life cherishing, then the chances of the arising of a new Hitler, Stalin or Pol Pot are reduced.

 

My Idea is no more then a one very first step for this goal and it is nothing but one of many other actions that should be made by governments, educational system, organizations, companies, communities and privet persons that have the common goal, which is to care day by day about the existence and moral/technical level of our civilization in order save and develop our life.

 

The logic that I am talking about is based on the essence of what we are as complex yet simple living things, that REALY try day by day find the best within them in any aspect of their life and then they choose to share it by an open dialog that can give them the ability to express themselves in non-destructive ways.

 

This internal/external dialog put any one of its participators in a better position that he was before the dialog.

 

As for my system, I only started to develop the first outlines of it, and it is hard to understood by any parson that believe that there cannot be any connection between morality and exact science methods.

 

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Since I realized that nobody here can grasp my ideas until now, so in the next post I show show examples of arithmetical operations, which are based on an included-middle reasoning and also connected to R.

[Guest Doron Shadmi]

By my included-middle axiomatic system ( http://www.geocities.com/complementarytheory/My-first-axioms.pdf ) there are two kinds of cardinals, two kinds of ordinals, and a scale factor, Which are used as the basis to define R and also my number system.

 

 

UC = Urelement Cardinal

 

QC = Quantitative Cardinal

 

IO = Internal Ordinal

 

EO = External Ordinal

 

SF = Scale Factor

 

Basic Scale factor is the ratio between 0 {.} or 1 {._.} to any other segment which is not 0_1.

 

Scale factor is {.} or any {._.} when it is used as the basic factor for the entire number system.

 

The basic arithmetical structure:

 

The first element of any arithmetic operation is always {.} or some {._.}.

 

The next parameter can be UC, QC, SF or a combination of them.

 

Any arithmetic always has a left to right direction of operations and the result of each pair is the basis of the next operation:

 

for example:

 

Addition and subtraction examples (only UC or {.} or {._.} are used):

 

0__2 + 0_1 = 0___3 (a new segment)

 

0__2 + 0_1.347… = 0____4.347…

 

{0__2} + {0_1} = {0__2, 0_1} (a new set of segments which its total length = 0___3)

 

{0__2} + {0_1.347…} = {0__2, 0_1.347…} (a set of segments which its total length = 0____4.347…

 

0__2 – 0_1 = 0_1 (a new segment)

 

0_1 – 0__2 = 1_0

 

0_1 – 0_1 = {}

 

0_1 – 1_0 = 0

 

1_0 – 0_1 = 0

 

1_0 – 1_0 = {}

 

1_0 – 1_0 – 1_0 = {} – 1_0 = -1_0 = 0_1

 

1_0 – 0_1 – 0_1 = 0 – 0_1 = 0_1

 

-0_1 = 1_0

 

-1_0 = 0_1

 

0 + 0 = 0

 

{0} + {0} = {0, 0}

 

0 - 0 = {}

 

{0} - {0} = {}

 

 

 

Multiplication and relations examples (QC or SF are used):

 

 

0__2 * QC3 = {0__2, 0__2, 0__2}

 

0___3 * QC2 = {0___3, 0___3}

 

The two results above are noncommutative (only if QC is used).

 

0_.5 * QC2 = {0_.5, 0_.5} (a set of segments which its total length = 0_1)

 

0_.5 * SF2 = 0_1

 

 

0__2 * SF3 = 0______6

 

0___3 * SF2 = 0______6

 

0__2 * SF0.5 = 0_1

 

-0__2 * SF0.5 = 1_0

 

 

0__2 / QC2 = {0_1, 0_1}

 

0__2 / SF2 = 0_1

 

0__2 / SF.5 = 0____4

 

0__2 / SF3.14…(PI) = 0__2/PI (and if we want we can notate it by a single symbol like 0__2/PI=@)

 

 

Also we can combine QC and SF for example:

 

0__2 / QC3 SF.14… = {0__2/3/SF.14…, 0__2/3/SF.14…, 0__2/3/SF.14…}

 

0__2 / SF.14… QC3 = {0__2/SF.14…/3, 0__2/SF.14…/3, 0__2/SF.14…/3}

 

 

 

0__2 / SF.14 = 0__2/SF.14…

 

X / 0 = {__}

 

0 / X = 0 (where X not= 0)

 

 

As for a sqrt(2) (for example), it is the ratio between x-axis and y-axis identical segments and we do not need Dedekind's Cuts for this.

 

 

IO and EO can be seen by using my new number system:

[MandrakeRoot]

Many wars have been the result of fear or Jealousy or other human emotions and not technology. Even in the time we were fighting with swords the wars were pretty gruesome. Secondly i disagree about the fact that universities do not teach there students about "moral" issues. Many of them have included obligated courses of Sustainable developpement and other courses allowing students insight into what their "discouveries" might create.

 

Moreover why should we use "morality" in for exemple Hahn-Banach's Theorem or Riesz representation theorem ?

These are abstract theorems and abstract maths costs only paper (if you sustainably cut wood this should not pollute ), the problem is applied mathematics for any technologic developpement that may pollute a lot (or kill everybody or whatever).

So my point here is that it is not the math system that is immoral but those that use it for "bad" causes !

 

Mandrake

[Guest Doron Shadmi]

Many wars have been the result of fear or Jealousy or other human emotions and not technology

And this is exactly what I am talking about.

 

No weapon execute itself' date=' and it is totally depend on our moral/reasoning abilities not to use it.

 

So we have to do the best we can in order to develop our internal properties, in order to avoid war.

Moreover why should we use "morality" in for example Hahn-Banach's Theorem or Riesz representation theorem ?

No theory exist without us so if we can understand them we have to do the best we can in order to use their insights to help us to survive, in this is my interpretation to morality, in this case.

 

Again, when I say morality i mean: our best reasoning in order to survive by using non-destructive ways.

[e(ho0n3]

Not to be petulant or anything, but I don't think (judging from the responses) anybody will satisfy your requirements Doron Shadmi. You say "No theory exist without us so if we can understand them we have to do the best we can in order to use their insights to help us to survive...". How does the Pythagorean Theorem, say, help me find food to eat? It doesn't. How does morality help me find food to eat? It doesn't either. I don't see where this is going.

[MandrakeRoot]

In fact the theories exist without us, it is just that we have to realise they do !

Well anyway that is some point of view about theorems and lemmas etc....

 

Ofcouse we have to use the theories we have developped for the best use for everybody. I am sure nobody will disagree with you on that, it is like a universal truth !

 

I would say like e(... That the theorems are not "immoral" or anything, they are just statements, like a sentence. Everybody that uses them will use their own morality in order to judge whether or not the outcome of his work will be worth while...

So in fact it would suffice that all scientistist are moral beings, doing all for the better of the world right ?

I still dont catch why there should be morality in theorems like Hahn-Banach or Pythagorean theorem ?

These are abstract statements....

 

Morality should help though in the search for food e(...) normally that should prevent us from putting 1.000.000 chickens in a 10 square meter cage or cutting their beaks because they will hurt each other ! (Hey i would too if i would be stuck in 10 square meter with so many other people )

But then again science has nothing to do in this judgement, theoretical science is without morality, it is the application where morality is desired in order to "create" "correct" things.

 

Mandrake

[Guest Doron Shadmi]

In fact the theories exist without us' date=' it is just that we have to realise they do !

Well anyway that is some point of view about theorems and lemmas etc....

[/quote']

Just now you gave an example of "power over nature" (or "existence beyond nature") point of view.

 

When you say: "In fact the theories exist without us" , on what "FACT" you actually you are talking about?

 

In my opinion (and please show me where I am wrong) what you call a "fact" is nothing but the subjective interpretation of formal or platonic points of view, where both of them are based on "power over nature" idea or "existence beyond nature" if you will, and both of them leading us to (in my opinion) irrational point of view of what I call "hard reality of surviving".

 

In short, what you call “fact” is nothing but the current paradigm of our civilization about exact science and its language.

But then again science has nothing to do in this judgement, theoretical science is without morality, it is the application where morality is desired in order to "create" "correct" things.

Again, it is nothing but the current paradigm of our civilization, which is based on combinations of "power over nature" + "existence beyond nature" ideas.

 

We should change (in my opinion) this interpretation in order to survive reality.

 

We should change (in my opinion) this interpretation in order to survive reality, where "correct" things are first of all to save and develop the complexity of life in non-destructive methods.

 

And no one but ourselves has to find an use these methods.