The traditional mathematician here is not aware of his\her use of direct perception in order to determine a given axiom.
He simply doing it by using partial brain skills, only the verbal_symbolic one.
As a result his\her reasoning can't comprehend Whole\Parts relations, which is achieved only if verbal_symbolic AND visual_spatial brain skills are actually unified.
The best you can get depends on how you are using your brain. Since you are partially using it about the discussed subject, then what I put in seems nonsense for you.
Furthermore, your axiomatic attitude about the considered subject is that there is no connection between your brain functions and deduction, which is indeed nonsense.
The traditional mathematician here is not aware of his\her use of direct perception in order to determine a given axiom.
He simply doing it by using partial brain skills, only the verbal_symbolic one.
As a result his\her reasoning can't comprehend Whole\Parts relations, which is achieved only if verbal_symbolic AND visual_spatial brain skills are actually unified.
The best you can get depends on how you are using your brain. Since you are partially using it about the discussed subject, then what I put in seems nonsense for you.
As I've said before I'm more than capable of understanding diagrams. It is not my fault that you think there is some magic to be obtained from a diagram that is somehow "beyond symbolism" because there clearly isn't when it's clearly possible to link the two supposedly disparate "mechanisms".
Furthermore, your axiomatic attitude about the considered subject is that there is no connection between your brain functions and deduction
There is no necessary connection between my brain functions and mathematical deductions. You want to argue the brain has primacy over mathematics in the universe you'll have an uphill struggle to say the least.
I really wish you would get the difference on these simple concepts. Which is exactly the same reason why jamming words together with underscores and saying, "using this magic reasoning skill will allow mathematics to be different than it's defined to be," is going to fail every single time.
If your next reply will be still from this artificial limitation,
As I've said before I'm more than capable of understanding diagrams. It is not my fault that you think there is some magic to be obtained from a diagram that is somehow "beyond symbolism" because there clearly isn't when it's clearly possible to link the two supposedly disparate "mechanisms".
There is no magic here. There is simply natural complementarity of your verbal_symbolic AND visual_spatial brain skills, which enables you to deduce better than any deduction that is derived separately form these skills.
Show me what that means in formal logical terms. No amount of diagrams, pictures etc... will be more convincing to me than the cold logic of a Turning Machine clicking through its tape.
There is no necessary connection between my brain functions and mathematical deductions. You want to argue the brain has primacy over mathematics in the universe you'll have an uphill struggle to say the least.
There is no "primacy over mathematics in the universe".
Your brain is simply an ongoing phenomena of the evolution, which is ancient as the universe itself, and this brain is exactly the way of the universe to be aware of itself.
Mathematics is nothing but some aspect of this developed awareness.
You still get the concept of brain only by its personal subjective aspect, and as long as this is your awareness of brain you simply unaware of its universality, which is non-personal.
As long as your awareness is unable to unify its subjective (personal) AND objective (non-personal) aspects, it gets things partially.
For example, your awareness can't define Ethical reasoning (in terms of evolutionary scale) AND Logical reasoning as a one comprehensive framework (whether it is abstract, or not).
If after B____ comes C_____, then after ?_____ comes ?______
You still get the concept of brain only by its personal subjective aspect, and as long as this is your awareness of brain you simply unaware of its universality, which is non-personal.
If after B____ comes C_____, then after T_____ comes U______
Your brain is simply an ongoing phenomena of the evolution, which is ancient as the universe itself, and this brain is exactly the way of the universe to be aware of itself.
There is no magic here. There is simply natural complementarity of your verbal_symbolic AND visual_spatial brain skills, which enables you to deduce better than any deduction that is derived separately form these skills.
There is no magic here. There is simply natural complementarity of your verbal_symbolic AND visual_spatial brain skills, which enables you to deduce better than any deduction that is derived separately form these skills.
The traditional school of mathematics is an agreement among minds, which exclude themselves as factors of their mathematical work.
The members of such school of thought can't pass the Mirror Test of any healthy self aware creatures.
The technology that is derived from non self aware creatures easily can be used as a self destruction tool of its unaware developers.
Organic Mathematics is one of the ways to bring back self awareness as an essential property of any scientific work, including the mathematical science.
The traditional school of mathematics is an agreement among minds, which exclude themselves as factors of their mathematical work.
The members of such school of thought can't pass the Mirror Test of any healthy self aware creatures.
The technology that is derived from non self aware creatures easily can be used as a self destruction tool of its unaware developers.
Organic Mathematics is one of the ways to bring back self awareness as an essential property of any scientific work, including the mathematical science.
Recently, Cecilia Heyes (Professor of Experimental Psychology, Oxford) has advanced the theory that mirror neurons are the byproduct of associative learning as opposed to evolutionary adaptation. She argues that mirror neurons in humans are the product of social interaction and not an evolutionary adaptation for action-understanding. In particular, Heyes rejects the theory advanced by V.S. Ramachandran that mirror neurons have been "the driving force behind the great leap forward in human evolution".(Ramachandran, 2000)[39] http://en.wikipedia.org/wiki/Mirror_neuron#Doubts_concerning_mirror_neurons
The right connection between complex creatures like us and the non-entropic realm, which enables our further development.
The traditional school of thought does not have this essential understanding, and as a result it does not understand Ethics (in terms of evolutionary scale) and its complementation with Logical reasoning.
Without this complementation, we are not going to survive the power of further manipulations of Nature's forces, like any collection of minds that fails to pass the Mirror Test (which according to it, the tested mind recognizes its reflection as something that belongs to itself).
This self recognition is the basis of resposibilty of self aware creatures, which enables them to avoid self destruction.
Nonsense like "There is no necessary connection between my brain functions and mathematical deductions" is a clear signature of an unaware mind, which can't take any responsibility on its expressions, whether they are abstract or not.
The right connection between complex creatures like us and the non-entropic realm, which enables our further development.
The traditional school of thought does not have this essential understanding, and as a result it does not understand Ethics (in terms of evolutionary scale) and its complementation with Logical reasoning.
Without this complementation, we are not going to survive the power of further manipulations of Nature's forces, like any collection of minds that fails to pass the Mirror Test (which according to it, the tested mind recognizes its reflection as something that belongs to itself).
This self recognition is the basis of resposibilty of self aware creatures, which enables them to avoid self destruction.
Nonsense like "There is no necessary connection between my brain functions and mathematical deductions" is a clear signature of an unaware mind, which can't take any responsibility on its expressions, whether they are abstract or not.
The traditional school of thought does not have this essential understanding, and as a result it does not understand Ethics (in terms of evolutionary scale) and its complementation with Logical reasoning.
Nonsense like "There is no necessary connection between my brain functions and mathematical deductions" is a clear signature of an unaware mind, which can't take any responsibility on its expressions, whether they are abstract or not.
Doron, since you are unable to point to any results from your use of Organic Mathematics(tm), can you point us to anyone who you agree has understood them and applied them?
ETA - since we all appear to be replying from our partial/verbal_symbolic brains, are we all going on ignore?
Doron, since you are unable to point to any results from your use of Organic Mathematics(tm), can you point us to anyone who you agree has understood them and applied them?
ETA - since we all appear to be replying from our partial/verbal_symbolic brains, are we all going on ignore?
Actually the cover of the book doesn't say what you've noted; it says, "Tips for Science Students," instead. Look again:
Be careful trying to understand Organic Mathematics - it has a tendency to distort reality. There was a poster here who sincerely tried to penetrate Doron's mind in order to extract reason behind his statements that concern very abstract and difficult philosophical issues concerning the development of mathematics. Within a week or two, the poster began repeatedly flushing the toilet in anticipation of a miracle.
Are math students really irrelevant to mathematics?
They do not significantly affect the development of math, but some of them do later on. So there is a teaspoon of relevancy, don't you think?
Right. Since every person can be typified (forall P: P(x) = t), mathematics actually doesn't require people, and that's the essence of Organic Mathematics - it's the fundamental truth that Doron wanted you and everyone else to understand. That seems to be paradoxical, because Doron has blamed people for depriving mankind of true understanding of mathematical logic due to the millenia of ignorance. But paradoxes cannot be fully understood without anyone digesting the notion of "types." The history of the Russell's paradox, oftentimes mentioned by Doron, clearly shows that anyone pondering the dilemma becomes sooner or later aware of the necessity to incorporate "types" into the thinking process, as Bertrand Russell readily found out: Russell's own response to the paradox was his aptly named theory of types.Recognizing that self-reference lies at the heart of the paradox, Russell's basic idea is that we can avoid commitment to R (the set of all sets that are not members of themselves) by arranging all sentences (or, equivalently, all propositional functions) into a hierarchy. The lowest level of this hierarchy will consist of sentences about individuals. The next lowest level will consist of sentences about sets of individuals. The next lowest level will consist of sentences about sets of sets of individuals, and so on. It is then possible to refer to all objects for which a given condition (or predicate) holds only if they are all at the same level or of the same “type.” http://plato.stanford.edu/entries/russell-paradox/
It becomes apparent that the statement Mathematics does not require people of a certain type is boring all the way to the cemetery, because it can be either proved or disproved - providing "types" is not consistent with the continuum. However, the statement Mathematics does not require people of any type leads to a challenging paradox that can be decided. A few steps down the hall of the cerebrum waits a surprise: the decision actually undermines the indestructible principle of causality! That, in turn, can buy the ticket to the past in order to change the present. And that's what Doron's genius has been after lately. Fortunately for most of us here, the tech aspects of such a travel will keep the ancestry of all who have questioned the soundness of Organic Mathematics safe.
As long as one defines the power of the Continuum in terms of collections , one does not understand a fundamental principle of the mathematical science, which is: The Whole is not the sum of parts.
By being aware of this fundamental principle one actually has the access to understand open systems, which are entropic-free and provide the optimal conditions for further development of complex self-aware phenomena.
We are some expression of this further development, and our brain reflects this development if it actually unifies Whole\parts relations in daily life.
The actual unification is done by using the subjective brain skills (which are characterized in terms of collections of strict or non-strict ids) and the objective brain skills (which are characterized in terms of the whole that is used as the invariant principle of given collections) as a one comprehensive framework, such that the observed, the observer and the tool of observation are unified.
One of the signatures of this unification is the brain's ability to deduce by using its verbal_symbolic AND visual_spatial skills.
Moreover, this brain ability actually fulfills the possibility to establish The Science Of Awareness, where one of its fundamental abilities is to actually bride Ethics (in terms of evolutionary scale) AND Logical reasoning, in order to (at least) survive further manipulations of Nature's forces.
Wrong. The traditional mathematicians have been mainly busy to investigate unknown identities by solving various equations. So they do have a head start with the new exciting field that you christened... (oops) that you named The Science Of Awareness. Let me explain...
Awareness can be likened to a certain type of acknowledgment. For example, it's unlikely that you would miss the following two lines of text.
1 + 1 = 2
o + o = O
But some folks may become aware of the possibility that both lines featuring identities (implied by the presence of symbol '=' ) are related. The awareness comes from a daily experience. For example if you want to take two carpets from two small rooms and lay them down beside each other flat, you need to bring them into a larger room.
Yet there are still some folks out there who would become aware of the fact that the two lines of identities don't run in sync with the context, and they would alter them this way:
2 = 1 + 1
S = s + s
It's easy to see what the context is.
Science of Awarness
Now it takes a traditional mathematician to uncover an inconsistency in the positional alignment that of course involves the name of the inventor of the new, promising scientific field.
Science of AwarnessDoron Shadmi
What inconsistence are we talking about here?
Well, according to the descriptive formula UPPER CASE = lower case + lower case,
(1) D = m + i
is a correct statement, but since mathematicians often use letters as a substitution for numbers, D = m + i is an incorrect statement. But where is the proof of the incorrectness?
Well, if a statement that includes '+' is incorrect, then a statement that includes the opposite; that is '-', must be correct. Therefore
(2) D = m - i
That's logically sound reasoning, but it hardly constitute any proof, because the letters involved can be substituted by any numbers and that means the initial identity D = m + i can be both correct and incorrect depending on the type of numerical substitution. But since we are aware of the fact that letters live in the alphabet and are particularly organized there, we substitute accordingly and from
we see that identity (1) is incorrect, as far the traditional math is concerned. It really deals with definitions and not mere descriptions. That means the alignment is not good - the field of the study and its author are not compatible.
Well, Doron, your attempt to invent Science of Awareness as a legitimate field of math-related study doesn't look good through the eyes of a traditional mathematician. But don't give up - your attempt can be still categorized. Here is the alignment once again...
S=cience of Awarnes+s 'proportional description and correct D=oron Shadm+i 'natural definition and incorrect.
But having an "incorrect" inventor is not really the point. The point is being aware of what the beginning and the end of the both aligned names can offer. From that, it can be shown that your Science of Awareness is even below a religion.
I am the Alpha and the Omega, the First and the Last, the Beginning and the End.
Revelation 22:13
Pay attention to the letters at the beginning and the end of names and use this identity
o o = less awareness
O O = more awareness
REveLATION 22:13
"Well, that's very good, Your Most Divine Awareness."
The phrase "... some folks may become aware of the possibility that both lines featuring identities (implied by the presence of symbol '=' ) are related." is exactly the limited awareness, which according to it the whole is a sum of given parts.
Moreover, this limitation holds even if this phrase was taken from a mambo jambo humorless nonsense reply.
Generally, if one challenging a traditional mathematician to use his\her mind in order to get things beyond the agreed reasoning, you get something like: "I cannot - you are proposing something that does not fit into standard arithmetic."
In other words, Mathematics for traditional mathematicians is already perfect in terms of verbal_symbolic-only-reductionist notion.
In their case Mathematics has nothing to do with the essence of Science, which is its ability to be developed according to the principles of Evolution, which is essentially creative, non-predictable and has a room for the linkage among the objective\subjective accepts of the developer, as a significant factor of a given result that is first of all the ability to unify Ethics (in terms of evolutionary scale) AND Logical reasoning, as a one organic and ever developed (abstract or non-abstract) realm.
The verbal_symbolic-only-reductionist notion is too weak in order to comprehend that.
This weakness is essentially shown in this phrase: "I will, however, remind you that real Mathematics continues to work; your stuff, not so much.".
The weak reasoning of this mind can't comprehend the devastating results that may emerge from works, which are unbalanced by Ethics (in terms of evolutionary scale) AND Logical\Technological skills.
The weak reasoning of this mind can't comprehend the devastating results that may emerge from works, which are unbalanced by Ethics (in terms of evolutionary scale) AND Logical\Technological skills.
The weak reasoning of this mind can't comprehend the devastating results that may emerge from works, which are unbalanced by Ethics (in terms of evolutionary scale) AND Logical\Technological skills.
Why do you hold back with that "may?" Just make it clear that if the content of your sermon isn't accepted as the unquestionable truth, the entire world goeth to hell - with no possibility of parol.
You are failing to see that the influence of Christianity, as a monotheistic system of belief, on mathematics fizzled. Hilbert's vision of "one mathematical god" taking care of all proofs got blurred by Godel and later Turing. That's why you should stop and revert to paganism, because pagans invented civilization and also 1 + 1 = 2. Yes, it is only one expression, but it also comprises five symbols. What else has this type of relation?
Well, for example, any one word that comprises five letters. And so we put all such candidate words into a box, mix them thoroughly, and pick up randomly the example word. And the word is... PROOF!
Ain't that coincidental?
It wasn't probably for Russell and Whitehead who suspected the intervention of the God of Deliberate Coincidences, and so they decided to make sure that those irrational, sacrifices-making pagans were actually right about their claim that 1 + 1 = 2, and so both noted mathematicians blessed the expression with a reason:
That proof made lots of folks sleep much better due to the appeal to the authority, which, albeit secular, works like a miracle. So I would recommend that you put on some academic credentials to support the content of your links.
The traditional fundamental notion of transfinite cardinality of a given set is that its size is bigger than any possible member, which is included in this set.
By using verbal_symbolic AND visual_spatial brain skills, the concept bigger than is not understood only in terms of the number of elements, as done by using verbal_symbolic-only interpretation of Cardinality.
For example, by using also visual_spatial brain skills Cardinality is not the size of a given set but it is the common property (the objective whole) of partial (and therefore subjective) aspects that no one of them can be used as the common property (the objective whole) for the rest of the partial (and therefore subjective) aspects of that common property.
An example: No member of the collection of all red things (where each one of them is a subjective aspect of this property) is the common property of being red (which is the objective aspect of this property).
Another example: No member of the collection of all sizes (where each one of them is a subjective aspect of this property) is the common property of being a size (which is the objective aspect of this property).
By using verbal_symbolic AND visual_spatial brain skills, we get the following generalization of the examples above as follows:
No member of the collection of all things with X property (where each one of them is partial\particular (and therefore) subjective aspect of X property) is the common X property (which is the objective (the whole) aspect of Whole(=objective)\parts(=subjective) unification).
Verbal_symbolic-only skillers can't comprehend Whole\parts unification, as clearly seen by their last replies, because they still get Unity in terms of Polychotomy.
Moreover, Whole\parts unification is beyond their reasoning, and therefore can't be used as a factor of their framework.
Here is how a verbal_symbolic-only skiller is satisfied: "That proof made lots of folks sleep much better due to the appeal to the authority,"
As long as that given proof is not a result the a reasoning that is derived from Ethics (in terms of evolutionary scale) AND Logical\Technological brain skills of creatures that are aware of their influence on the (abstract or non-abstract) environment, these creatures do not have the luxury "to sleep much better", simply because no reasoning that is derived from partial brain skills, actually passes the Mirror test (where one passes only if it is aware of the results of its work, on its external and internal environments).
A phrase like "Better yet: There's nothing that my "thing" can do that can be done easier with current mathematics other than obfuscation." is done by a mind, which simply refuses to be aware of the possible devastating results on daily life, as an impact of its mathematical work (responsibility is thrown to the trash can, without any chance to be recycled).
A phrase like "Why do you hold back with that "may?" Just make it clear that if the content of your sermon isn't accepted as the unquestionable truth, the entire world goeth to hell" demonstrates the inability of that mind to get Uncertainty.
A phrase like "Better yet: There's nothing that my "thing" can do that can be done easier with current mathematics other than obfuscation." is done by a mind, which simply refuses to be aware of the possible devastating results on daily life, as an impact of its mathematical work (responsibility is thrown to the trash can, without any chance to be recycled).
Words are cheap - why not try actually doing something that would actually produce devastating results on daily life like other people who've done so I'd actually care to pay attention to.
It's hilarious watching you squirm, doron. You've got nothing. And you know it. I don't understand how a nuclear reactor works, but sure as hell can appreciate the electricity that's obviously coming from it.
What's coming out of doronetics? And no, I'm not interested in word salads. A few decades should be enough to have something better.
A phrase like "Why do you hold back with that "may?" Just make it clear that if the content of your sermon isn't accepted as the unquestionable truth, the entire world goeth to hell" demonstrates the inability of that mind to get Uncertainty.
I think that your critical conclusion clearly demonstrates your inability to properly count and categorize. Why do you hold back with that "may?" Just make it clear that if the content of your sermon isn't accepted as the unquestionable truth, the entire world goeth to hell are two (2) sentences which you've managed to reduce into one (1) phrase. That reminds me the relentless reductionist effort of Christian missionaries who were gingerly reducing the number of pagan gods into a bare pluralistic minimum (God of Sentence1 and God of Sentence2) and then, on one nice summer afternoon, they announced to the indigenous that there was actually only one god to pray to and His name was Phrase. Since the ability to properly count and categorize is a must for anyone who has decided to tinker with the set theory, I would recommend that you practice in this direction, before using your visual_spacial brain skills to envision mathematical apocalypse taking place in May of an uncertain year.
Your insight into the relation between the whole and its parts doesn't seem to work that well in real life, as I have found out. Since you only mentioned that the whole is not the sum of its parts, but failed to disclose if it is less or more, I decided to conduct an experiment to find out about that. Basically, I began cutting whole numbers into parts, summing the parts thereafter:
11 into 1 and 1 --> 1+1=2 --> 2 is less than 11
123 into 1 and 2 and 3 --> 1+2+3=6 --> 6 is less than 123
666 into 66 and 6 --> 66+6=72 --> 72 is less than 666
After about ten thousand repetitions with different whole numbers, I was ready to propose a conjecture that the whole is always larger than the sum of its parts. Since the last whole number I cut into pieces was
16926261 into 16 and 9 and 26 and 26 and 1,
I got inspired by that and decided to test my conjecture accordingly...
So I ordered the whole pizza and then asked Giuseppe to cut it into slices. Since, according to the conjecture, the sum of parts is less than the whole, a noticeable discount was under way, right?
Once again, according to the reductionist reasoning of the traditional mathematicians here, the whole is a sum of parts, no matter if these parts appear as a living organism (in that case we deal with the whole concept) or a set of quantified chemical elements, which are closed in separate boxes (in that case we deal with the sum concept).
Whole and sum are not the same concept, simply because the whole has a quality that can't be quantified, as can be done with the sum concept, but reductionist minds are too weak in order to comprehend that (for example, to know the qualitative difference between a living organism and a pizza).
If one counts the quality of the whole, then one may say that the whole is more than the sum of given parts, but by doing it, this one actually measures quality in terms of quantity, and as a result one actually misses the quality of the whole, which can't be defined in terms of sum.
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