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Is the P=NP Problem an NP Problem?

What I’m going to say is going to be unpopular, but I cannot reconcile my own well-being without giving you an answer to this problem from my perspective.

My only reason for reluctantly writing this, knowing what kind of reaction I could receive is, because I abhor that some of the best minds on our planet are occupying themselves with this problem. It pains me to no end to see humanity squandering its power for a problem that, as it is currently framed, is unanswerable. It goes further than this though. There will come a time when questions such as this one will be cast upon the junk heap of humanity’s growth throughout history. It will take its rightful place along such ideas as phrenology.

Here’s why I say this:

The problem is firmly and completely embedded in Functional Reductionism. I say this, because the problem’s framing requires us to peel away the contextual embedding of the problems for which it is supposed to clarify.

This is just one of its problems. Here’s another:

Since the data for this problem (and those like it) are themselves algorithms, they are compelled to be functionally reduced versions of mind problem solving (varying types of heuristics and decision problems) which reduces the problem’s causal domain and its universe of discourse even further. How can a specification based upon functionally reduced data be again used as data for the problem’s solution in the first place?

That means that this problem has no independent existence nor causal efficacy. Everywhere I have looked at this problem, the definitions of NP-Hard and NP-Complete do not lead to proving anything useful. We cannot ‘generalise’ the mind by reducing it to some metric of complexity. Complexity is also not how the universe works as Occam’s Razor[1] shows.

I am prepared to defend my position should someone have the metal to test me on this. Another thing: I wish I could have left this alone, but we all need to wake up to this nonsense.

[1] http://bit.ly/2GHbRkW How Occam’s Razor Works

[Quora] http://bit.ly/2EuRdP3

Getting Hypertension About Hyperreals

HyperReals(Links below)

This system is quite interesting if we allow ourselves to talk about the qualities of infinite sets as if we can know their character completely. The problem is, any discussion of an infinite set includes their definition which MAY NOT be the same as any characterisation which they may actually have.

Also, and more importantly, interiority as well as exteriority are accessible without the use of this system. These ‘Hyperreals’ are an ontological approach to epistemology via characteristics/properties we cannot really know. There can be no both true and verifiable validity claim in this system.

https://www.youtube.com/watch?v=rJWe1BunlXI (Part1)
https://www.youtube.com/watch?v=jBmJWEQTl1w (Part2)

“How much knowledge does the understanding in words contain?”

hermandadblanca_universo-mente-fractal-geometria-sagrada

Words are symbolic indications and/or conveyors of meaning and are not that meaning in themselves.

Meaning is found, stored, and manipulated in our minds. This is why different languages are capable, in varying degrees of usefulness, to convey meaning which is very similar to that found via the symbols of any other.

déjà vu 01

It It is also the reason why there are words indicating meaning that are not found in other languages; or, if found in a different language, the other language requires more of its own structure, dynamics, and resonance to convey the same meaning.

dèja vu 02

For example: the words ‘déjà vu’ in French are found in German ‘schon gesehen’ and in English ‘already seen’, but these phrases do not convey the full meaning found in the French version. To counter this deficit, their meaning in other languages must be ‘constructed’ out of or ‘fortified’ by the careful use of longer strings of symbols. This additional construction and/or fortification may even fail at times. This is often where the word phrase from a different language is simply added to the language in which the concept is missing.

This same situation is found in the literature of many languages. The words used to convey meaning are condensed and may contain more meaning than is usually the case. In this regard, even the person reading/hearing the words may not possess the competence necessary to catch this condensed meaning in its fullness.

Mathematical expressions, albeit more precise, are also indications of meaning. They are more robust in their formulation, but at ever-increasing depth or scope, even they may fail to reliably or conveniently convey meaning.

dèja vu 03

Our understanding of what words mean is not always accurate, but where our mutual understanding of the meaning of words overlaps, and the degree to which they overlap, is where their meaning can be shared.

Our own personal understanding of words is measured by our ability to apply their meaning in our lives.

There is also a false meme, which I would like to clarify.

“Knowledge is Power!”

It is wrongly said that ‘Knowledge is power’. The truth is another: Knowledge is the measure of usefulness of what we understand and is the only true expression of its ‘power’.

The value of Knowledge is found in its usefulness and not in its possession.

My Quora Answer

Which questions does Category Theory help us answer?

Category 02

Another chapter in my attempt to help break the ‘spell’ of the category theoretical ‘ontologicisation’ of our world.

This may seem to many as a purely academic question, but we all need to realise that all of what we consider a modern way of thinking rests upon ‘mental technologies’ such as Category Theory.

Academics are literally taking the ‘heart’ out of how our world is being defined!
If we don’t pay attention, humanity will continue losing its way.

Category theory is a wonderful and powerful tool; nevertheless category theory, with all of its utility, is purely ontological. It can masterfully answer questions such as ‘Who?’, ‘What?’, and ‘How?’.

Category 01

However; it is regretfully inadequate to form a comprehensive representation of knowledge, for it lacks expression of epistemological value, which are the very reasons for is use. Epistemology is about answering the questions of ‘Why?’, ‘What does it mean?’, ‘What is my purpose?’,…
Answers to questions of this kind are implicitly supplied by us during our consumption of the utility afforded by category theory. We often are so beguiled by this power of categorical expression that we don’t realise that is we ourselves who bring the ‘missing elements’ to what it offers as an expression of knowledge.
It does a wonderful job with exteriority (ontology), but cannot sufficiently describe nor comprehensively access interiority (epistemology). Therefore, it has limited metaphysical value with respect to philosophy in general.

Interiority 08

Philosophies of mind, of language, or of learning are not comprehensive using only category theoretical tools.
Categorical structures are highly portable, but they can describe/express only part of what is there. There are structures, dynamics, and resonance that the ontology and functionalism in category theory completely turns a blind eye to.
More general than category theory is knowledge representation. It includes and surpasses category theory in many areas, both in scope and depth, but in particular: knowledge representation includes not just the ontological aspects of what we know, it goes further to describe the epistemological as well.
The qualities of Truth, Goodness, Beauty, Clarity,… can be defined and identified within a knowledge representation if the representation is not restricted to ontology. When category theory is used for the purpose of defining qualia, the objects must first be ontologised and functionally reduced. Trying to grasp them with tools restricted to category theory (or even semiotics) is like grasping into thin air.

 

Category theory, although very powerful, is no match for the challenge of a complete representation of knowledge. Category theory will tell you how to tie your shoes, but it can’t tell you why you are motivated to do so.

Lateral Numbers – How ‘Imaginary Numbers’ May Be Understood

Rbi0Y

First, allow me to rename theses numbers during the remainder of this post to lateral numbers, in accordance to the naming convention as was recommended by Gauss. I have a special reason for using this naming convention. It will later become apparent why I’ve done this.

If we examine lateral numbers algebraically, a pattern emerges:

i^0 = 1

i^1 = i

i^2 = -1

i^3 = -i

i^4 = (i^2)^2 = (-1)^2 = 1

i^5 = i \cdot i^4 = i

i^6 = i^2 \cdot i^4 = (-1)(1) = -1

i^7 = i^2 \cdot i^5 = (-1)i = -i

i^8 = i^4 \cdot i^4 = (1)(1) = 1

When we raise lateral numbers to higher powers, the answers do not get higher and higher in value like other numbers do. Instead, a pattern emerges after every 4th multiplication. This pattern never ceases.

All other numbers, besides laterals, have a place on what currently is called the ‘Real number line’.

I qualify the naming of the Real Numbers, because even their conceptualisation has come into question by some very incisive modern mathematicians. That is a very ‘volatile’ subject for conventional mathematicians and would take us off on a different tangent, so I’ll leave that idea for a different post.

If we look for laterals on any conventional Real number line, we will never ‘locate’ them. They are found there, but we need to look at numbers differently in order to ‘see’ them.

Lateral numbers solve one problem in particular: to find a number, which when multiplied by itself, yields another negative number.
Lateral numbers unify the number line with the algebraic pattern shown above.

ComplexNumbers Example 001

2 is positive and, when multiplied by itself, yields a positive number. It maintains direction on the number line.

ComplexNumbers Example 002 - Negative

When one of the numbers (leaving squaring briefly) being multiplied is negative, the multiplication yields a negative number. The direction ‘flips’ 180° into the opposite direction.

ComplexNumbers Example 003 - Negative Squaring

Multiplying -2 by -2 brings us back to the positive direction, because of the change resulting in multiplying by a negative number, which always flips our direction on the number line.

So, it appears as if there’s no way of landing on a negative number, right? We need a number that only rotates 90°, instead of the 180° when using negative numbers. This is where lateral numbers come into play.

ComplexNumbers Example 004 - Negative Squaring using lateral numbers01

If we place another lateral axis perpendicular to our ‘Real’ number line, we obtain the desired fit of geometry with our algebra.

When we multiply our ‘Real’ number 1 by i, we get i algebraically, which geometrically corresponds to a 90° rotation from 1 to i.

Now, multiplying by i again results in i squared, which is -1. This additional 90° rotation equals the customary 180° rotation when multiplying by -1 (above).

ComplexNumbers Example 004 - Negative Squaring using lateral numbers

We may even look at this point as if we were viewing it down a perpendicular axis of the origin itself (moving in towards the origin from our vantage point, through the origin, and then out the back of our screen).

[If we allow this interpretation, we can identify the ‘spin’ of a point around the axis of its own origin! The amount of spin is determined by how much the point moves laterally in terms of i.
We may even determine in which direction the rotation is made. I’ll add how this is done to this post soon.]

Each time we increase our rotation by multiplying by a factor of i, we increase our rotation another 90°, as seen here:

ComplexNumbers Example 004 - Negative Squaring using lateral numbers03

and,

ComplexNumbers Example 004 - Negative Squaring using lateral numbers04

The cycle repeats itself on every 4th power of i.

We could even add additional lateral numbers to any arbitrary point. This is what I do in my knowledge representations of holons. For example a point at say 5 may be expressed as any number of laterals i, j, k,… simply by adding or subtracting some amount of i, j, k,…:

5 + i + j +k +…

Or better as:

[5, i, j, k,…]

Seeing numbers in this fashion makes a point n-dimensional.