Topic: Making PoW usefull (Read 6578 times)

Once and for all, you are irrefutably rebutted:

An interesting fact is that the Möbius strip and the Torus are topologically related.


The Möbius ladder might help demonstrate this a bit better.

http://upload.wikimedia.org/wikipedia/commons/7/71/Moebius-ladder-16-animated.svg

Which brings us to the Hopf fibration, that's where the fundamental existential "twist" is hidden.

http://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Hopfkeyrings.jpg/250px-Hopfkeyrings.jpg

A couple more pages and we will finally be getting to the point of making PoW useful!

Earth’s set of all real numbers is, essentially, a Möbius strip fashioned from a line where one surface extends from 0⁻ to −0⁻, the other from −0⁺ to 0⁺, and all “edges” are retained.

So, the existence [of the limit] would be equivalent of saying "as above, so below", which is a realization that "now" is the only time and "here" is the only place [in all of existence].


This would then be "as within, so without", which means that Earth's "nought" and Earth's "zero" are one and the same, but neither actually exists (thus strict inequality) because it's the hole in The Torus?


So, if neither "nothing" nor "everything" exists, then only the "twist" is real. I guess "the Vortex of the Torus" would be an appropriate description of Earth's numerical system then.  

Your “existential paradox” (VectorChief) arises from the notion that hyperreality’s nothing (here, nought) and everything (here, zero) “exist” (Stover) (i.e., are “elements of” the real).

I see. It's getting trickier down the road, as we are probably approaching some existential paradox here.

Singularity (one zero) leads to things being undefined (division by zero).
Duality (two zeroes) necessitates trinity (three zeroes) with neutral balance point between the two, or otherwise addition lacks commutativity (-1+1 != +1-1).

Maybe those "interdimensional" modifiers provide a way out of this, because placing two zeroes (or three for that matter) on a single numerical line would always necessitate something in between: (a+b)/2.

The way I look at Earth's numerical system (according to how you describe it) is more like a pair of gears or maybe even spirals placed next to each other, rather than a single numerical line. Maybe this approach doesn't require addition to be commutative, because the time arrow is always forward and every moment in existence is unique (see my signature) so there is no way to get the same perspective (number) by following two different paths (order of addition)?

I guess the following quotes by Kurt Vonnegut would be appropriate here:

"Everything is Nothing with a twist."

https://s-media-cache-ak0.pinimg.com/736x/0f/24/16/0f2416cafb8738b50ab815863360a0d0.jpg

"So it goes."

Direction of approach can be used to determine what might otherwise be indeterminate.

The answer to -1+1 that I held in mind was −0⁻ + −0⁺, which would not be reducible further in Earth's numerical system, but would represent zero under conventional mathematics. This makes addition commutative:

−0⁻ + −0⁺ = −0⁺ + −0⁻ = −0  <-  not on the axis, but rather an imaginary bridge?

When it comes to subtraction, we get the following:

−0⁻ - −0⁺ = −0⁻ + −0⁻ = −0⁻
−0⁺ - −0⁻ = −0⁺ + −0⁺ = −0⁺

Subtracting polarized nought from non-polarized nought would destroy the bridge resulting in polarized nought of opposite sign. Adding it would be equivalent to subtracting with sign inverted. Subtracting polarized nought from itself should reestablish the bridge resulting in non-polarized nought.

This in fact adds a three-state modifier to all non-zero numbers as well, something that conventional mathematics didn't have due to its zero being singular (thus adding/subtracting it had no effect). It should look like this:

1 + −0⁻ = 1⁻
1 + −0⁺ = 1⁺
1 + −0  = 1

Which reminds me of the (past, present, future) modifiers used in conjunction with numbers in the new type of numerology (described here, scroll all the way down to Numerology).



In your example: -1+1 = −0⁻ < −0⁺ = +1-1  =>  -1+1 < +1-1
Does Earth's addition commute? Is strict inequality due to implied modifiers?

PS: Also you might have mixed the terms positive and negative in your description.

In the first cases, one approaches nought from the negative direction. In the last cases, one approaches nought from the positive direction.

You got me intrigued with Earth's numerical system. The name sounds just about right and it is hidden under layers upon layers of onion router, exactly like those zeroes loop around the infinity.

I will look into that.
Does it shake the foundations of math so badly that it gets banned if published in the open?

Also what would be the result of -1+1? Which of those inner zeroes?

If a limit of a transcendental number should be converted to Earth’s numerical system, the both should equal each other without exception.

Interesting.

So, for a given macrostate the microstates represent an inner world, while other macrostates represent an outer world. The inner world can also be seen as a multiplicity of choices one could make, which would then translate into the multitude of parallel realities one would simultaneously exist in (according to each outcome of a choice). The fact that complex numbers have "real" and "imaginary" parts might have something to do with the above, while "rational" and "transcendental" would correspond to behavioral patterns. Transcendental numbers are particularly interesting as they are finite in magnitude, but infinite in structure.

I wonder what happens when infinity is introduced into the picture? Would it mean that a singular infinite intelligence is equivalent to an infinite number of finite intelligences and the essence that connects all of the "copies" is the Identity or the presence of "I"? Everybody is "I", and that's the same "I" as in the Infinite, that's the ultimate sameness in our otherwise difference, the sameness that everyone can wake up to. Feel the stillness of "I" in you, for that is the absolute Is-ness of existence shining through. There is no opposite to being "I", as there is no opposite to existence.

These might be relevant to this discussion in general:
https://www.youtube.com/watch?v=5FELdBsixGg
https://www.youtube.com/watch?v=3yFiqdCjNMk
https://www.youtube.com/watch?v=PwSvV3RAH4s

(Red colorization mine.)



“Th[ose] other ‘[you][𝗌]’” (VectorChief) would be the unique arrangements (i.e., microstates) of “the dice” (Nave) that satisfy a definition of “[you]” (i.e., a given macrostate).

Yeah, I guess I see it. You can actually fit a whole another numerical sub-system in between the inner zeroes in the middle, in which they will serve as the outer ones (bigger than infinity). Or in other words, one singular zero in our current system suddenly "wakes up" as the whole numerical system in itself. That's what I was referring to in my example, only your zeroes have never gone to sleep .

Yep! That's the image I held in mind when talking about self-similarity. Though I apply the concept in a broader sense. If the first reflection brings some amount of entropy, then all sub-sequent ones will only increase it. Thus this self-similarity will replicate not only the rule but also the exception, as the original must have contained both as a whole (see the quote below).


The first reflection is achieved by asking the paradoxical question: "is there me out there, which is not me?". This other "me" needs to be different in some regards, but similar in structure in order to constitute another "me" in a wholistic way. In other words, if the original was autonomous, the reflection would need to be autonomous as well. So it's not a perfect copy in a physical sense, but rather a meta-physically wholistic one with fundamental attributes of the original preserved, but different in all other aspects (made in the image of).

I think, Bitcoin-Litecoin pair is a good example of the first true reflection. By looking at their differences and similarities we can actually judge which of Bitcoin's characteristics are fundamental and which aren't. The PoW-scheme is fundamental, though a particular hashing function is not. They both share limited amount of coins, though the limit itself is different. The emission curve is identical and thus fundamental, but Litecoin started later, so it's phase differs compared to Bitcoin.

It really is God-The-Father (Bitcoin), God-The-Son (Litecoin) and God-The-Holy-Spirit (People) kind of relationship at its finest. If Bitcoin recognizes itself in its son, people should too and many do. Second coming, anyone?

http://67.55.97.103/wp-content/uploads/2014/08/litecoin-gocoin.jpg

Love & Light!


I wonder if symbols of hyper-reality actually experience themselves as sentient beings? If they do, then it is real for them, and we are just outside observers of this sort of flat-land reality of its own. You might be interested in watching the following video (if haven't yet seen): https://www.youtube.com/watch?v=dEaecUuEqfc

(Red colorization added.)

“Earth’s numerical system” (username18333) “loops around” at both its −0 (under conventional mathematics, zero) and its 0 (under conventional mathematics, undefined).

(Red colorization mine.)


(All emphasis mine.)

(Red colorization mine.)

That's very insightful. Thanks!

So, if applied to my frequency spectrum example, the 0-frequency flat-line of non-existence at the bottom, which all non-zero frequencies can sample and thus refer to (as we do now), is actually a whole another reality-bubble of existence within itself (with its own 0 and infinity), which cascades this way further and further indefinitely. Thus the idea of becoming non-existent can only be experienced momentarily, as this state immediately brings forward the realization that you're suddenly everything there is, which then cools down towards a particular finite shape, so that the whole process can repeat itself again and again.

Of course, this analogy is somewhat simplistic in its one-dimensionality. First comes realization, that vibrational spectrum is multi-dimensional and then that it is actually infinitely-dimensional. So, while physicalized material part of existence might go through a regular birth and death cycles, it is possible that some parts of consciousness maintain a particular frequency band orthogonal to that, and thus constitute "soul".

The Riemann zeta function is definitely an interesting object, as it has something to do with reality of physical matter. Recent research has demonstrated that certain characteristics of it resemble the trajectories of physical particles (bounces on the left) and their spiral-shaped tachyon traces (on the right). Which brings forward the idea that matter actually has memory, which in turn gives rise to consciousness. Or maybe it's the consciousness that gives rise to matter via mathematics?

http://kniganews.files.wordpress.com/2013/01/bc52matiyas.jpg

It becomes more and more evident, that mathematics, consciousness and matter are the three inter-related parts of the same one thing. It goes like this: mathematics is shaped by consciousness, consciousness is shaped by matter, matter is shaped by mathematics. Circular dependency that attempts to resolve itself in the ever-lasting "now".

http://kniganews.files.wordpress.com/2012/11/equ123.jpg

It somehow also reminds me of the Shield-of-Trinity picture a few posts above, which hints at the idea of what that "one thing" can actually be.

Colorization is good! Colours are victorious over the grey, you're gonna love this one 4 just 1 day.

I sort of see what Baudrillard is saying, as it is more applicable to our fiat money forms and their countless derivatives, though I'm convinced now that they played a certain role in society to bring us to where we are. It's time to recognize that and move forward towards something more solid. Like Bitcoin with its PoW-secured blockchain, which is grounded in reality via its non-trivial hashrate component.

I prefer to think that states live within me, than the other way around, and for that I love and respect them.


Gold -> fiat -> Bitcoin -> crypto-fiat? -> ...?

Incompatible paradigms alternate in time (usually with some overlap), that's how reality solved one of its contradictions. By studying one branch of self-similar system, one can contemplate the idea of existence itself and one's place in it. Hyper-reality might be one of those branches, but it's hard to say what's real and what's fiction. It's a mystery!