Updated some stuff, the first topic has an image now so you don't need to parse what I said.

Fractal Conjectures:

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A popular feature of fractals is the supposed infinite perimeter, while I do not disagree with this, I do offer an extension to it. Being that the perimeter of a fractal does have a finite version, that it behaves less like a 1 dimensional quantity, and more like an area. If you were to take two squares, and removed every other infinitely thin slice from one of them, what is the difference. One’s perimeter is infinite, in fact it isn’t even an enclosed shape. Here is where things get interesting, if you added up all the segments of the second square, to a 2 dimensional area, it would approach half that of the untouched square. Finite area. I propose a similar way to quantify fractals, if you were to crumble of the perimeter of the fractal, it would approach a value no greater than the area which encloses the fractal:

A shape’s perimeter is no greater than the area that encloses it, when the dimensions of the two quantities differ positively.

This suggests that while it isnt very intuitive that an infinite quantity can approach a finite one, it does, and is a way to quantify them.

A shape’s perimeter is no greater than the area that encloses it, when the dimensions of the two quantities differ positively.

This suggests that while it isnt very intuitive that an infinite quantity can approach a finite one, it does, and is a way to quantify them.

Removing Time from Math:

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So a lot of math operations require you to perform a calculation over time, I am trying to remove that. I want to skip the whole middle and get right to the end, like saying "draw a square" and instead of using one line to calculate the next, I just draw the whole square. I have already done this to an extent on one of my favorite equations; the linear congruential pseudo-random number generation equation. It looks like this: The next number = multiplier * previous number + increment modulated by the modifier... Well this is what I have now: the nth number is the limit as k approaches the multiplier (((k^n)*(first number * k + increment - first number) - increment)/(k-1)) mod the modifier.

So far it works with what I have tested (positive integers), its a 0-time formula for the starting formula, it can calculate any part of a pseudo random number sequence, you can even modify it by removing the modifier and it still works for non-modified sequences. If it does break down tell me pls. I have been working on giving it an exponent, as in a sequence like next=previous^2 and such, it is much tougher, I am getting close though... I just haven't had time recently to work on the formula. Also please tell me if you have seen this done before or have I created something unique? I have plenty of picture evidence of my math if I need to submit it somewhere. I find it very useful since whenever I try to code my own "space engines" that are small, I use these formulas, but I always would have to create a list of pre-generated numbers to work off of, because the time it took to calculate a list... But this would allow no time to calculate the pseudo random number lists, and by applying a function to make negative numbers asymmetric to positive ones, and a limit (density), you can create a star map, or more... I don't know if there is a better method though... Well thats all I have time for,

Now with an image!

So far it works with what I have tested (positive integers), its a 0-time formula for the starting formula, it can calculate any part of a pseudo random number sequence, you can even modify it by removing the modifier and it still works for non-modified sequences. If it does break down tell me pls. I have been working on giving it an exponent, as in a sequence like next=previous^2 and such, it is much tougher, I am getting close though... I just haven't had time recently to work on the formula. Also please tell me if you have seen this done before or have I created something unique? I have plenty of picture evidence of my math if I need to submit it somewhere. I find it very useful since whenever I try to code my own "space engines" that are small, I use these formulas, but I always would have to create a list of pre-generated numbers to work off of, because the time it took to calculate a list... But this would allow no time to calculate the pseudo random number lists, and by applying a function to make negative numbers asymmetric to positive ones, and a limit (density), you can create a star map, or more... I don't know if there is a better method though... Well thats all I have time for,

Now with an image!

A Conjecture on Math over Time

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This goes along with "Removing Time from Math", so equations, formulations, calculations, and sequences of various kinds, all share time. It takes time to perform a calculation, time to simulate, time to anything... But this does create an interesting conclusion. These actions are not outside of time, and time itself is not bound to cause and effect, being cause and effect. So i would argue that there is a "static" equation for every equation over time. An equation that plots the shape of the cause and effect without performing the cause and effect. If true in every possibility then it might be something that could out-compute any possible computer. Imagine a computer that takes formulas and finds their static versions, as I did in the topic above. Now instead of performing the calculations to get the answer, it just skips straight to the answer. Like how instead of plugging in the previous number to get the next, over n iterations, I could just say what is it at nth iteration. Instead of an n-body simulation where every next step is calculated, the entire thing is converted to a static version, where the future to infinity can be observed, and there is no difference (besides for one being timeless). Its the difference from plotting a y=x function by plugging in a number and finding the next with it to just plugging in for x. You give it a problem and you skip to the solution, no in between... Like how a game could have an entire universe but not load it all, but also the entire future of it determined prior... What will simulated civilization do 1 million years in the future? Instead of simulating it just plugs in a +1 million years and BAM! There it is... No in between. I have yet to see any reasons to why this cannot be done, unless entropy cannot be predicted or graphed, which I doubt.

Imaginary Number Issues [Possibly Solved]

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Possible Fix:

Old Argument:

I am starting to suspect that imaginary numbers are not true 2nd dimensional numbers as they fall in and out of the real plane. They are also based on a constant of 2, hence (-1)^(1/2). The reason I am questioning this is that I am working on a number "line" that treats infinity as a number, I have worked out transformations across this number "circle" and how each angle relates to the other side. But the math always broke down with imaginary numbers whenever I tried to convert my "circle" into a sphere... It kept becoming hyperbolic and the relations kept breaking down... Thats when I thought "maybe imaginary numbers are not in a true extra integer dimension, rather somewhere in between" since they do not act like how one should. i*i= -1 instead of i^2 (yes thats the same but you'll get the point)... This then got me thinking... Imaginary numbers have a lot of weird quirks... Thats when I realized that we never "solved" square root (-1)... We just said "Hey! Its i! We did it! Its solved!" like saying root(5) equals g because you don't know how to find root(5)... I'm not saying there is a true answer to this... But it looks off... All of the implications from imaginary numbers seem fine though, just not the 2nd dimension aspect. Maybe I'll put my observations on infinity and how it acts like a number, hmm...

Old Argument:

I am starting to suspect that imaginary numbers are not true 2nd dimensional numbers as they fall in and out of the real plane. They are also based on a constant of 2, hence (-1)^(1/2). The reason I am questioning this is that I am working on a number "line" that treats infinity as a number, I have worked out transformations across this number "circle" and how each angle relates to the other side. But the math always broke down with imaginary numbers whenever I tried to convert my "circle" into a sphere... It kept becoming hyperbolic and the relations kept breaking down... Thats when I thought "maybe imaginary numbers are not in a true extra integer dimension, rather somewhere in between" since they do not act like how one should. i*i= -1 instead of i^2 (yes thats the same but you'll get the point)... This then got me thinking... Imaginary numbers have a lot of weird quirks... Thats when I realized that we never "solved" square root (-1)... We just said "Hey! Its i! We did it! Its solved!" like saying root(5) equals g because you don't know how to find root(5)... I'm not saying there is a true answer to this... But it looks off... All of the implications from imaginary numbers seem fine though, just not the 2nd dimension aspect. Maybe I'll put my observations on infinity and how it acts like a number, hmm...

An Observation On Reality

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Stepping back from all the math, knowns, and constants, I wanted to start looking at the world from the ground up again. To see if I could come to any newfound observations. I would argue that I have. I asked myself, "What is the most fundamental things in the universe", well... I got 'Location' and 'Identity'; what something is and where. But there was something missing... Time... You can state a location in time, but an object or identity cannot exist in a location in time, as it is a continuous part of time. This makes time an identity, not a location. I can't 'drop' and object into time and say "Thats where it is", instead it branches out, flowing, looping, into an entire structure. I then asked "Well, what if there was no time?", then we see that identity goes away. You become unable to identify anything, how do you know if a particle is an electron or positron? How can you tell that light is moving at all? If an object is going left or right? If there is gravity? Mass? It all goes away... So there, like a system, are locations in time, but time itself is an identity. Particles get their identities from their 'shape' in time. How they move together. But then you realize... The where aspect is pretty flexible too... Locations are dimensions but not magnitudes or shapes, those are identities. Place two particles next to each-other in spacetime and you get some coiling system over time, forever. The nature of the particles only revealed by their hidden identity, a temporal identity. An electron isn't just an electron but it is also what it does. Things are things and what they do. Where they are and where things happen is not an identity but the what

*is*. But what defines a system? The complete identity? Well... that would be every interaction forever. Aside from an event horizon, everything would share a common identity. The entire universe is an identity. But what is location in all of this? Isn't it part of the universe? The medium that gets filled? Location+Identity? Well if Location+Identity=Everything, then Everything-Identity=Location? Do the event horizons get left out of all this? Or are they just infinitesimal points where identity and location become the same thing? And would the inverse of such a singularity give rise to both location and identities? Meaning that the inside of the event horizon, from an outside perspective, is nothingness... Complete nothingness... A cancellation/combination of both locations and identities. But that would mean that the identity isn't lost...No information lost... Its like 2/3 + 1/3 = 1, the combination of location and identity yields nothing. But wasn't it suppose to equal everything? Well if the inverse of nothing is everything, that means the formula for everything is the inverse of nothing. 1/0 = infinity. 1/(Identity + Location)=Everything. Or perhaps its the other way around... Maybe it doesn't matter... All just a perspective. I will have to think on this... Like how does maximum movement through time give rise to the distinctions between time and space... How does this all connect. And how does a universe come out of this, like our own? It seems that it all goes back to time and identity... But what does that even mean anyways? Maybe I am looking at this too philosophically? Or perhaps the details slow down the eventual conclusion... Maybe you don't need pi and a radius to describe a circle... Pi and the radius could be anything, but yet you could still describe a circle... Perhaps I can describe the universe without knowing the constant of the universe. Like a variable... Perhaps...