1-1+1-1+1... - A Metaphysical Rant

[TJ Reeves]

Part of Actualizing yourself is learning about the spiritualities around the world.

One interesting spirituality is pythagoreanism, which takes numbers as god. Pythagoreans are basically the ultimate nerds.

From wikipedia:

Pythagoreanism originated in the 6th century BC, based on the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans, who were considerably influenced by mathematics and mysticism. Later revivals of Pythagorean doctrines led to what is now called Neopythagoreanism or Neoplatonism. Pythagorean ideas exercised a marked influence on Aristotle, and Plato, and through them, all of Western philosophy.

These days, it's hard to find pythagoreans out and about. The closest thing possible are the abstract mathematicians in some universities. They're not as crazy as the O.G. Pythagkreans, but if you press them hard enough, they will reveal personal beliefs that are way crazier than the existence of trolls, goblins, or fairies.

The perennial philosophy is that:

Absolute Truth = Undefined = You = God = Absolute Infinity = Zero

And the conclusions of the pythagoreans were no different from those of other mystics. It just happens to be that they reached their enlightenment through math. That is why I consider them full fledged spiritual practitioners in the vein of hardcore buddhists. I mean would you rather sit for 4 hour of zazen or 4 hours of high level calculus? 

The cool thing about the pythagoreans (or their modern equivalents) is that they bear the truth out out in clear terms. I mean, when it comes to talking about stuff, math is about as clear and logical as it gets. 

But most people don't grasp what's going on because the implications of math are too insane. That is, normal people would rather feel comfortable than accept the straight up Truth. Thats why pythagoreans were so fucking hard core. 

Take a pencil and a piece of paper and follow along to see what I mean.

------

Step 1: 0 = 0  

Basic level stuff here. 

Step 2: 0 = 1-1 = (1-1) = 0

Nothing too crazy. Just create and destroy to return to the same place. We can do this as much as we want.

Step 3: 0 = 1-1+1-1+1-1... = 0

In case you're confused, let's add brackets to make things easier to look at.

0 = 1-1+1-1+1-1... = (1-1)+(1-1)+(1-1)... = (0) + (0) + (0) + (0).... = 0 

We still end up with Create and destroy, create and destroy, create and destroy...

Brackets are arbitrary... we can put brackets however we'd like. 

Step 4: 1-1+1-1+1-1... = (1-1)+(1-1)+(1-1)... = 1+(-1 +1)+(-1+1)...

All I did was change the position of one of the brackets -- nothing that breaks the rules of mathematics. 

Step 5: 1+(-1 +1)+(-1+1)... = 1+(0)+(0)+(0)... 

Wait a minute. This is starting to get fishy...

Step 6: 0 = (1-1)+(1-1)+(1-1)... = 1+(-1 +1)+(-1+1)... = 1+(0)+(0)+(0)...  = 1

No... That can't be right... Let me check that again... That would mean...

Step 7: 0 = 1

No. It can't be!

-----

Oh yes. And things only get crazier from here...

Lets say the letter S represents the same infinite, alternating series of plus and minus 1 from earlier. 

Step 8: S = 1-1+1-1+1-1... 

Now lets play around. What is (1 - S)? Just insert numbers into the equation to see.

Step 9: 1 - S = 1 - (1-1+1-1+1-1...)

Multiply every bracketed number by the negative sign. 

Step 10: 1- S =  1-1+1-1+1-1...

Didn't we say that S = 1-1+1-1+1-1... in the first place?

Step 11:  1 - S = S 

So if we move things around to the other side to solve the equation we get

Step 12: 2S = 1

divide to finish the problem

Step 13: S = 1/2 = 1-1+1-1+1-1....

In review we have:

0     = 1-1+1-1+1-1... 

1     = 1-1+1-1+1-1... 

1/2 = 1-1+1-1+1-1... 

putting it all together we get solid logical proof for 

0 = 1/2  = 1 

In this way, the truth of even one of the most simple mathematical concepts is Absolutely Relative and based on your contextual perspective. 

Fuckkkk. We can't allow this. There has to be some solid answer. Lets keep going. 

Let's imagine a lamp that turns on and off

1 = the lamp is on

0 = the lamp is off

Then lets imagine ourselves turning the lamp on and off indefinitely. 

S = 1-1+1-1+1-1...  = On, Off, On, Off, On, Off...

This is called Thomson's Lamp, after a mathematician named James F. Thomson.  

The universe wants to know what Thomson's lamp looks like at the end of infinity. 

Oh you say we can't do that? That would take all of eternity, wouldn't it?

Actually it would just take one day. Or one hour. Or one minute. Or However long I'd like. 

Lets say I decided to figure out what's going on with Thomson's Lamp in under a minute. I would wait half of a chosen total time to turn the lamp on. Then I would wait half of that time to turn the light off. Then I would wait half of that half to turn the light on again. And so on and so on over the course of just one minute.

I can match each step in turning the lamp on and off to each half intervals of the total time I chose. After an infinitely smaller set of intervals, I will have an infinite number of steps.

This would be called a super task. 

Step 1: ON -  Total Time passed: 30 seconds

Step 2: OFF - Total Time passed: 45 seconds

Step 3: ON -  Total Time passed: 52.5 Seconds

Step 4: OFF - Total Time passed: 56.25 Seconds 

Step 5: ON -  Total Time passed: 58.125 Seconds

... infinite number of times ...

Step 5: ??? -   Total Time elapsed: 1 minute

Thomson had this to say about his lamp's state at the end of the minute:

It seems impossible to answer this question. It cannot be on, because I did not ever turn it on without at once turning it off. It cannot be off, because I did in the first place turn it on, and thereafter I never turned it off without at once turning it on. But the lamp must be either on or off. This is a contradiction.

Thomson jumped the gun when he says his example demonstrates a 'contradiction.' 

See, I'd like you to bear with me when I say that life isn't so black and white. Indeed, life as we know it happens in the undefined state of 1/2, where the lamp isn't ON or OFF even though it can be none other than ON or OFF. 

Here is a graph of the on off lamp where 1 = On and 0 = Off

What we can do is take the theoretical infinite limit of the series. Limits are basically a way to say "alright, where is this stuff headed?" 

Usually, limits require convergence, or a clear direction for the graphed out representation. What you'd end up doing is taking that convergence and finding the average of its direction. 

As you can see in the above graph, however, the lamp is in a state of ON or OFF such that it has no convergence. If anything there is divergence. 

That's fine. Math allows us to keep looking at bracketed versions of the series and take the average of all of the answers and then take the average of that average.

In normal people talk, just look at the little line I placed in the average of the graph: it's 1/2. 

If you still don't understand, watch this video:

When looking at this sum Thomson had this to say:

Now mathematicians do say that this sequence has a sum; they say that its sum is 1⁄2. And this answer does not help us, since we attach no sense here to saying that the lamp is half-on. 

Lets look at this lamp in real life:

Most everyday lamps don't turn on and off at an infinitely fast rate. They go through a partly-on and partly-off state. So the real world version of the lamp would never quite be on or off at end of our little time interval. 

Moreover, if the lamp were able to turn on and off at an infinitely fast rate, it would still appear ON to us despite having an average of 1/2.

To understand what I mean, look at pulse-width modulation (PWM) works for dimming lamps. PWM lights turn on and off thousands of times per second, causing eyes and cameras to sample a mix of on and off time and average the two. When you "dim" the lamp, you actually just change the amount of time that goes by between ON flickers and OFF flickers. 

The key is that since eyes and cameras work by sampling light at a certain rate and pasting images together, you don't realize that there's any flickering going on at all.

Again, in fast motion, it just looks like a light that's on. So, 1/2 looks like 1 and not so much like 0, although it is indeed just at 1/2.  

That's just the surface level.

-----

Isn't it just a little sketchy that I claimed to complete an infinite task in a finite time as if it were a piece of cake? 

I intentionally ignored the significance of what was going on.

We all do. 

See, every moment of our day is itself a super task. 

Think about it for a moment:

• when you walk across the street you have to walk across half of the street
• when you walk across half the street you have to walk across half of the half of the street
• when you walk across the half of the half of the street you have to walk across half of the half of the half of the street.
• and so on towards infinity

Thus we have an infinite amount of steps taken in a finite time. This is called Zeno's Paradox.

Scientists handwave the paradox away by saying that reality "stops" at the Planck length, planck time, and light signals of the observable universe, but metaphysically, that is bullshit. (What happens when we cross half a planck length?  and half of that? etc...) Moreover, we don't just quantize reality as a way to talk. We do so unconsciously from the very moment we are born. It's necessary to have a minimum limit to the size of time and space or else we could not function whatsoever. 

The human brain itself seems to localize and quantize infinite awareness. (read: does not create, but instead localizes!) It takes pure infinite energy and pure infinite time and pure infinite imagination and makes it a finite form of energy, time, and imagination. It's like an anchor for pure nothingness to believe it is pure everythingness. 

The brain does this over and over again at a certain frame rate such that reality gets created and destroyed and created again without us noticing. 

You know how movies have a frame rate of about 24 frames per second? We have a frame rate too. Although the eye itself does not have an on and off switch similar to a camera, our entire being itself has a frame rate. Otherwise, we would be stuck going through infinity at every moment. 

This frame rate is what determines our estimation of time's passage.

Again, if you increase the frame rate, you would get a slowed down reality. If you decrease the frame rate, you would get a faster reality. 

The smaller you cut up time, the slower it gets. If you cut it infinitely small, you get infinite time. If there are no cuts then there is simply infinity. 

If you don't believe me, try to swat a fly. Small insects cut up, or quantize, reality at a greater rate than we do and for that reason, they have ridiculous reaction times. Their 'frame rate' is around 250 Hz while ours is about 60 Hz. For that reason, flies see us swatting them at about 1/4th the speed we think we do and they easily escape. 

So to be clear again, time itself is infinitely smooth. But to experience this you would have to take an infinite amount of time, which is simply not feasible for a normal creature. 

The solution is that our brains cut up time and space into distinct units to bootstrap time and get it going.

This 'cutting up' makes reality "pop" in and out of existence every moment. The flickering of creation and destruction gets glazed over so that it all looks like one smooth thing. We would not function very well if we saw everything flickering in and out of existence while time passes from one moment of now to the next moment of now. 

The same general idea applies to why we don't perceive objects as probability clouds, but instead newtonian objects. We would not function if everything we saw 'existed' as a probability cloud. Imagine looking in your lovers eyes only to see right through their head because they are in fact made out of 99.9999% vacuum! 

So, we unconsciously make it look like:

• the lamp is On
• reality is real
• objects are solid
• you are "you"

When the truth is that:

• the lamp is in a non dual state, both On and Off 
• reality is in a non dual state, both real and not-real
• objects are in a non dual state, both waves and particles
• you are in a non dual state, both you and not-you 

----

And it goes further. Lets look at the big bang and cosmic inflation and apply our little numbers for a second by saying

0 = a state of nothingness

1/2 = a state in-between nothingness and oneness 

1 = a state of ultimate oneness

Now,

1 -- Lets "start" with the big bang for a moment. This would be like a state of '1.'

We're talking about an infinitely large universe packed into a space that was smaller than a cosmic string. 

We're talking about a state where all matter and all possibilities and all of existence were packed together in something smaller than all of matter and all possibility and all of existence. 

This is uncalculatably low entropy. It's as mystical as it gets to think that this level of entropy could have ever happened. Its up there with the greatest mysteries of the world. 

Just think about what it would take to gather up so much stuff in one small, highly ordered space. And I thought it took forever to set up a game of Jenga!

1/2 --- Then we have a never-ending inflation outward. Everything explodes outwards at a faster and faster rate forever. This creates stars and planets and ultimately Us. 

We walk around thinking about it, aware of our impending doom looming around the next step, constantly taking action to do something about this doom. 

0 --- No matter what, the inflation continues such that every atom is becomes totally separate from all other atoms. Space is at an unimaginable level of high entropy.

This is the heat death. This is zero. There is nothingness. 

There is so much nothingness that the notion of time itself is a Kosmic joke. If I record a video of the universe over the course 1 planck time, 10 years or 1 google years and play back the video over an interval of 10 seconds, everything will look the same. At this moment, it doesn't matter what happened any more --- all of history erases itself. 

Something strange happens.  A new bubble of oneness - aka a new big bang happens. Even if there's a 1/googol chance of this happening, it would happen because who gives a fuck we have all of eternity to do it. 

From Caltech Physics, Cosmology, and Philosophy professor Sean Carroll's audio course Mysteries of Modern Physics -- Time:

"Although it might be very rare to fluctuate 100 billion galaxies, it may not be that difficult to fluctuate the tiny region of space that is dominated by super–dark energy and is ready to inflate.

○   Imagine we have empty space, nothing but vacuum energy and the very cold thermal radiation we expect because of quantum mechanics. Random thermal fluctuations occur all the time.

○   Because space itself is flexible, perhaps the shape of space can be fluctuated. Perhaps a small bubble can be pinched off that is full of dark energy and ready to inflate. That little bubble can inflate, expand, reheat, and look exactly like our Big Bang.

○   In this way, what we thought was equilibrium—a state of maximum entropy—could be shown not to be equilibrium. We can always increase the entropy of the universe, according to this way of thinking, by creating new universes that split off and go their own way, and this process continues forever."

A related scenario is that the purpose of conscious evolution itself is to induce such universal pinching off! Some call this the omega point.

Imagine if we (or some 'other' conscious beings somewhere at some time) are put here on this universe to help create the type of hyper dimensional superconsciousness that could induce a universal bubble after our own deaths. 

Or imagine that we create a supercomputer that creates a supercomputer that simply recreates the universe through simulation.

Or imagine creating some form of a cosmic consciousness where calculations are made in a hyper dimensional place.

imagine that the cosmic bubble, the simulation, and the cosmic consciousness are the same fucking thing! 

Now imagine that this will happen at the end of our time. In particular, we take all of eternity to figure out how to pinch off a simulated baby-universe somehow.  

Then Imagine that this happened at the beginning of our time. In particular, it took someone or something all of eternity to figure out how to pinch off the baby universe that we exist in currently. It's the most unbelievable thing ever. 

Then imagine that it's happening right now as we gear ourselves up with computers, video games, and space missions for what seems like no good reason other than some weird idea of "progress" that no one can actually define but the smartest people all work toward.

Let's Go back to the scenario of a super simulation. Lets say this cosmic computer created a universe that looks basically identical to the one we live in. 

Imagine the hyper dimensional computer pinching off simulated minds within itself meant to explore the simulation it created. Imagine little robots it can send out with the sole purpose of gathering data -- little probes that can look and feel and touch things from a filtered perspective while figuring out how the hell to create a new universe.

To this Kosmic-supercomputer-mind's simulated perspectives within itself, objects look solid. But when these simulated perspectives look at objects with a microscope they reveal the objects to be 99.99999999% nothing because, again, they're just holographic simulated perspectives. (And by the way, there's no difference between 1 and 99.9999 repeated, so 99.9999 repeated nothingness is  100% nothingness).

To these simulated perspectives, all sensation would be a hallucination. To be clear:

Hallucination

- noun -

1. a sensory experience of something that does not exist outside the mind. 

Since every experience would always just be another part of mind, everything would be a hallucination.

Imagine that this hyperdimensional-Kosmic-Supercomputer-consciousness takes in all simulated perspectives to gather enough data to once again do the impossible. It manages to create - better yet be - that godhead known as the Big Bang Singularity after some time.

Except that, even the hyper dimensional-kosmic-supercomputer-consciousness a simulation!  

What I propose is that we are part of a mind at large that creates simulated holograms within itself to better understand itself before it once again dies and rebirths itself through yet another super simulated non dual existence. This mind at large is conscious and it is conscious of its own impending death and rebirth. And We - and this is a Kosmic We that includes all possible conscious creatures in all possible areas of the universe - are here to create the universe - to create god by inducing further consciousness somehow using our individual perspectives. This has happened before and this will happen again and this happens forever. The mind-at-large is just another part of what ends up forming an even larger mind that forms an even larger one.

We're talking mind-at-larges all the way up and simulated mind-at-larges all the way down. Turtles all the way up and turtles all the way down. 

We could go ahead and say that the universe just does this on its own spontaneously and so It doesn't need anyone. But what I'm saying is that we are what it looks like when the universe does this on its own. We are the spontaneous process. 

We have a universe that's created, destroyed, created, and destroyed over the course of eternity in many different ways. The path doesn't matter. The end state does. That end state gets reached through ever evolving life. 

And what does that end state look like after the course of eternity? It's somewhere in the middle of creation and destruction of course, just like Thomson's Lamp. 1-1+1-1+1-1+1...  = S = 1/2 = Undefined. It would be the place where the lamp exists between On and Off. It would have no end, it would have no beginning.

It would be us! We are what the end of eternity looks like! We're that in-between from the big bang to the heat death!

THIS IS IT! Welcome to the end of eternity, motherfucker! 

Which is fucking awesome - not only do we get an answer to what's going on with reality, we also get a fucking purpose! What better purpose is there than to a) increase your consciousness to b) increase the overall consciousness of everyone and everything to c) create God to d) create you and everything and everyone you've ever loved. You want immortality? You want happiness? You want purpose? You got it: you are your own parent, your own infinite creator traveling from life to life bootstrapping your non dual existence by chipping away with a quadrillion different chisels from a quadrillion different perspective to create a statue of yourself in a place of absolute nothingness! 

You are indistinct, indivisible, indestructible, incomprehensible, invaluable - truly incredible! Your job is to realize and manifest this incredibleness. 

And they say you can't derive an ought from an is.

We are in a state of both nothingness and everythingness glazed over to look like everythingness, just like the pulse-width modulated light. 

Each part of being has smaller parts forever. If you zoomed into at anything, it would disappear into deeper and deeper infinities. It would never have a place to stop. In this way, there's nothing but infinitely divisible parts that are made out of infinitely divisible nothingness. It is truly groundless.

Each whole gets nested within bigger wholes forever. If you zoomed out, you would never find a point where you see the whole thing. It could never be 'whole' because to be whole implies an end. So it wouldn't even have the possibility of reaching wholeness for there's always more to add.

Parts create wholeness except parts don't exist and wholeness don't exist. 

It would transcend zeroness and oneness and simply be non-dual. But we don't see it that way. We see it as naive reality consistent of solid, separate, whole parts with a finite size.  

*sigh* Actually, who am I kidding. These are all just speculations.

Plus, It's not like you'd understand. You'd rather stick to the paradigm that you know the limits of what's true or not true. You'd rather freak out about calling reality a hallucination. You'd rather hide yourself from the possibility that you're essentially stuck in the matrix. 

In other words, lets go back to arguing about about the nature of trolls. Certainly taking trolls seriously is far more insane than taking rigorous, pure mathematical logic seriously. 

Edited August 19, 2017 by TJ Reeves

[Max_V]

This is so interesting, thanks for sharing!

[ajasatya]

2 hours ago, TJ Reeves said:

Step 3: 0 = 1-1+1-1+1-1... = 0

be careful here. if you want to assume that the result of that sum is 0, then you have to describe its parcels more precisely. if you mean it to sum exactly 0, then the pattern should be said explicitly: "let's add an arbitrary number of +(1-1)'s", meaning that even though the number of 1's and the number of -1's are infinite, they are equally infinite because they grow in the same speed.

it completely crashes step 4 because it's impossible to replace the brackets like that. that algorithm of replacement is incompatible with the fact that the number of 1's and -1's are the equal.

edit: it's impossible to break arithmetics because it's built upon solid axioms. however, it's possible to notice its incompleteness. you might want to check out Gödel's incompleteness theorems for this.

Edited August 19, 2017 by ajasatya

[Erlend K]

Fun read?!

I used to love infinite series in college, but its been a few years, so Im not 100% sure I got this correctly. What I think is correct:

1-1+1-1+... = sum(-1)^n, from n=0 to i. This series is equal to 1 for all even numbers, and 0 for all odd numbers.

For lim i->inf (the Grandis series), the sum is 1/2, and not 0. Im not sure if it is possible to break the brackets like you do for an infinite series, but if you can, the aritmetic would be

1-1+1-1+... = 1+(-1+1)+(-1+1)+... = 1+ lim i->inf sum(-1)^(n-1), for n=0 to i, = 1 + the inverse of the Grandis series = 1 + (-1/2)  = 1/2. So the sum dosnt change. 

Edited August 20, 2017 by Erlend K

[hundreth]

Cool thread! Hope they shred your math to bits and let's see if it still holds up. Seems like another valid frame of reference to understand being, of which there appears to be many.

Math IS mystical as fuck. I'm not surprised you can find enlightenment and non dual awareness within it, just as one can find it by turning inward.

Edited August 19, 2017 by hundreth

[ajasatya]

23 hours ago, Erlend K said:

For lim i->inf (the Grandis series), the sum is 1/2

no. it's not a convergent series. theres no real number L for which lim_{n->inf} sum(-1)^n = L.