Variance is Fractal
 

You cant get a truthful picture of the "variance" of a thing unless you have the mean to that thing. If you do not document wins/losses and keep stats then you have no way of calculating your mean, variance or EV (unless you are annette_15).

(fixed variance) example: The mean (long run) win rate for AA vs KK HU seeing all 5 cards is 83%. A measured sample over say 200 games of a win rate of 72% is variance. The more sessions, or iterations the closer you get to the true "mean" of that thing. The mean is the truth of an equation. In this example the mean was the win rate of AA vs KK HU while seeing all five cards.

There is (fixed) variance (odds), and there is variance of your theoretical "edge" (dynamic) and tilt (dynamic)....

By using solid bankroll management, variance will rarely have you lifting an eyebrow unless you've been on tilt.

It often makes the hair on the back of your neck stand on end with or without tilt!

Re: Variance is Fractal
 

I don't think you know what fractal means.

Re: Variance is Fractal
 

EDIT: Forget the legit response, I recall this particular OP from another thread. It could get strange in here.

Re: Variance is Fractal
 

what do you want to say?

I like "By using solid bankroll management, variance will rarely have you lifting an eyebrow" though

Re: Variance is Fractal
 

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You cant get a truthful picture of the "variance" of a thing unless you have the mean to that thing.

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That depends entirely on the relative size of the mean and standard deviation. An error of 1% on the mean causes an error of 1% of the mean on the standard deviation. If the mean is small compared to the standard deviation (say on a one-day stock return), this is a trivial error and you can estimate the variance far more accurately than the mean. If the mean is large compared to the standard deviation (say on heights of healthy adult males), this is a large effect.

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If you do not document wins/losses and keep stats then you have no way of calculating your mean, variance or EV (unless you are annette_15).

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I half agree. You don't have to document anything, but you do have to keep some statistics. You don't need to record every hand result, but you should keep at least open, high, low and close bankrolls per session. I know of no way to compute poker win parameters without data.

[ QUOTE ]
(fixed variance) example: The mean (long run) win rate for AA vs KK HU seeing all 5 cards is 83%. A measured sample over say 200 games of a win rate of 72% is variance. The more sessions, or iterations the closer you get to the true "mean" of that thing. The mean is the truth of an equation. In this example the mean was the win rate of AA vs KK HU while seeing all five cards.

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Actually, AA beats KK 1,399,204 out of 1,712,304 times, for 81.7%. It also ties 7,923 times which gives equity (tie counts as half win) of 82.2%.

In this example, the mean (82.2%) is high compared to the standard deviation (37.8%). If you measure a 72% win rate for AA, you will estimate a 44.9% standard deviation. Your 14% error on the mean will correspond to a 41% error on the variance.

But this is only because you postulate a mean higher than the standard deviation. Suppose you measured the KK win rate instead of the AA win rate. Now your error on the mean is 57% (you measured 28% instead of the correct 17.8%). So now the error on the mean is larger than the error on the variance.

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There is (fixed) variance (odds), and there is variance of your theoretical "edge" (dynamic) and tilt (dynamic).... By using solid bankroll management, variance will rarely have you lifting an eyebrow unless you've been on tilt.

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I agree the first sentence is a reasonable way to analyze edge. The second is a matter of preference. If you play poker to grow your bankroll, it often makes sense to take risk with it. Poker without bankroll risk is called "penny ante." It's a fun game for kids and people who hate risk.

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It often makes the hair on the back of your neck stand on end with or without tilt!

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This seems to be the opposite of what you said above. If it's true for you, I suggest you shave your neck to get rid of the tell.

Re: Variance is Fractal
 

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Can you say Mandelbrot backwards?

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Can you explain what fractals have to do with simple variance?

Re: Variance is Fractal
 

[ QUOTE ]
[ QUOTE ]
You cant get a truthful picture of the "variance" of a thing unless you have the mean to that thing.

[/ QUOTE ]

That depends entirely on the relative size of the mean and standard deviation. An error of 1% on the mean causes an error of 1% of the mean on the standard deviation. If the mean is small compared to the standard deviation (say on a one-day stock return), this is a trivial error and you can estimate the variance far more accurately than the mean. If the mean is large compared to the standard deviation (say on heights of healthy adult males), this is a large effect.

[ QUOTE ]
If you do not document wins/losses and keep stats then you have no way of calculating your mean, variance or EV (unless you are annette_15).

[/ QUOTE ]

I half agree. You don't have to document anything, but you do have to keep some statistics. You don't need to record every hand result, but you should keep at least open, high, low and close bankrolls per session. I know of no way to compute poker win parameters without data.

[ QUOTE ]
(fixed variance) example: The mean (long run) win rate for AA vs KK HU seeing all 5 cards is 83%. A measured sample over say 200 games of a win rate of 72% is variance. The more sessions, or iterations the closer you get to the true "mean" of that thing. The mean is the truth of an equation. In this example the mean was the win rate of AA vs KK HU while seeing all five cards.

[/ QUOTE ]

Actually, AA beats KK 1,399,204 out of 1,712,304 times, for 81.7%. It also ties 7,923 times which gives equity (tie counts as half win) of 82.2%.

In this example, the mean (82.2%) is high compared to the standard deviation (37.8%). If you measure a 72% win rate for AA, you will estimate a 44.9% standard deviation. Your 14% error on the mean will correspond to a 41% error on the variance.

But this is only because you postulate a mean higher than the standard deviation. Suppose you measured the KK win rate instead of the AA win rate. Now your error on the mean is 57% (you measured 28% instead of the correct 17.8%). So now the error on the mean is larger than the error on the variance.

[ QUOTE ]
There is (fixed) variance (odds), and there is variance of your theoretical "edge" (dynamic) and tilt (dynamic).... By using solid bankroll management, variance will rarely have you lifting an eyebrow unless you've been on tilt.

[/ QUOTE ]

I agree the first sentence is a reasonable way to analyze edge. The second is a matter of preference. If you play poker to grow your bankroll, it often makes sense to take risk with it. Poker without bankroll risk is called "penny ante." It's a fun game for kids and people who hate risk.

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It often makes the hair on the back of your neck stand on end with or without tilt!

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This seems to be the opposite of what you said above. If it's true for you, I suggest you shave your neck to get rid of the tell.

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Good post Arron, clarified a few things for me. I used poker stove for the aa vs kk. The comment didn't refer to a session or any one group of things. More of a "looking back" chill watching the 15ft surf roll by. Some waves are shredable 10 footers while every now and then you catch and ride a monster. Whether you barely survive the wipe out or hold a 6 second barrel you'll always remember and "re live" it looking back, once the high/low is gone. Once you come back "home".

Re: Variance is Fractal
 

[ QUOTE ]
[ QUOTE ]
Can you say Mandelbrot backwards?

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Can you explain what fractals have to do with simple variance?

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Who said variance was simple?

Re: Variance is Fractal
 

Ok, explain how "variance is fractal".

Re: Variance is Fractal
 

The very nature of what variance "IS", is fractal. This makes every process both of the transparent and non transparent kind also fractal.

My point is that by knowing this and by being aware of this fractal nature of variance, we can consciously keep "the math" in harmony (which includes various "standard deviations" with various magnitudes) which can improve our game. I think that through a deeper understanding of what variance "is", we can all but remove the "tilt" factor which for most, is our biggest enemy.

By realizing that variance IS fractal, we take it out of a box that we have sub consciously put it in, which makes it tough to analyze and fix leaks un in an unbiased way (which should be a goal). By putting variance in perspective, we can see why anyone who "hates" variance is not a long term consistent winner, in this "game".

Re: Variance is Fractal
 

[ QUOTE ]
The very nature of what variance "IS", is fractal. This makes every process both of the transparent and non transparent kind also fractal.


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variance is due to randomness, fractals are not randomly generated

Re: Variance is Fractal
 

[ QUOTE ]
[ QUOTE ]
The very nature of what variance "IS", is fractal. This makes every process both of the transparent and non transparent kind also fractal.


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variance is due to randomness, fractals are not randomly generated

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actually fractals can be randomly determined, or deterministic. In some sense, I think the OP could be close to correct, though his thinking may be off a bit. The returns from a stock market can be approximated by fractals (once you remove the base 12% or so expected annual return), and I would think poker winnings would look fairly close to stock returns. I know most Sharkscope graphs look similar.

Though to be honest, I have no idea what that metaphysical BS is in the grandparent. Nor do I think applying a fractal process to the modeling of poker returns gives significantly better results than an approximation by a normal distribution. In the stock market example, the biggest difference in the two approximations is that the tails of the distribution of stock returns is slightly larger than expected from a normal distribution. But those are low probability events, and at least the downward swing of the negative outliers would probably be interrupted by a player stopping for the day or some other external factor.

Shane

Re: Variance is Fractal
 

[ QUOTE ]
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The very nature of what variance "IS", is fractal. This makes every process both of the transparent and non transparent kind also fractal.
"

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variance is due to randomness, fractals are not randomly generated

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The "randomness" is an element in poker and the variance on that is random. BUT this only when the cards themselves are randomly played. Since we can do anything from muck to shove, this game is hardly random.

Poker being a minus sum game (if played purely random) would have JUST normal variance. However, ,most topics of "variance" are talked about in a purely Linear model while 90% of the game is nonlinear, and chaotic.

Poker is not a minus sum game for all, due to the part of the game that allows for an "edge" to be possible. This part of the game IS nonlinear, and chaotic.

[img]/images/graemlins/shocked.gif[/img]

Re: Variance is Fractal
 

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
The very nature of what variance "IS", is fractal. This makes every process both of the transparent and non transparent kind also fractal.


[/ QUOTE ]

variance is due to randomness, fractals are not randomly generated

[/ QUOTE ]

actually fractals can be randomly determined, or deterministic. In some sense, I think the OP could be close to correct, though his thinking may be off a bit. The returns from a stock market can be approximated by fractals (once you remove the base 12% or so expected annual return), and I would think poker winnings would look fairly close to stock returns. I know most Sharkscope graphs look similar.

Though to be honest, I have no idea what that metaphysical BS is in the grandparent. Nor do I think applying a fractal process to the modeling of poker returns gives significantly better results than an approximation by a normal distribution. In the stock market example, the biggest difference in the two approximations is that the tails of the distribution of stock returns is slightly larger than expected from a normal distribution. But those are low probability events, and at least the downward swing of the negative outliers would probably be interrupted by a player stopping for the day or some other external factor.

Shane

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The outliers in the "tails" of markets bell curves are either unforeseen events and or manipulation.

The tails on a bell curve for poker hands and distributions is random of course are normal because all that is being measured is the fixed static odds of the cards playing out randomly.Since starting cards only matter to a small degree, naturally most of poker is fractal, thus, most variance is fractal.

P.S Whats with this comment here ---> "I have no idea what that metaphysical BS is in the grandparent."

What is this supposed to mean? Clarify please?

Maybe you and Tom are board pals?

Re: Variance is Fractal
 

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
The very nature of what variance "IS", is fractal. This makes every process both of the transparent and non transparent kind also fractal.


[/ QUOTE ]

variance is due to randomness, fractals are not randomly generated

[/ QUOTE ]

actually fractals can be randomly determined, or deterministic. In some sense, I think the OP could be close to correct, though his thinking may be off a bit. The returns from a stock market can be approximated by fractals (once you remove the base 12% or so expected annual return), and I would think poker winnings would look fairly close to stock returns. I know most Sharkscope graphs look similar.

Though to be honest, I have no idea what that metaphysical BS is in the grandparent. Nor do I think applying a fractal process to the modeling of poker returns gives significantly better results than an approximation by a normal distribution. In the stock market example, the biggest difference in the two approximations is that the tails of the distribution of stock returns is slightly larger than expected from a normal distribution. But those are low probability events, and at least the downward swing of the negative outliers would probably be interrupted by a player stopping for the day or some other external factor.

Shane

[/ QUOTE ]

The outliers in the "tails" of markets bell curves are either unforeseen events and or manipulation.

The tails on a bell curve for poker hands and distributions is random of course are normal because all that is being measured is the fixed static odds of the cards playing out randomly.Since starting cards only matter to a small degree, naturally most of poker is fractal, thus, most variance is fractal.

P.S Whats with this comment here ---> "I have no idea what that metaphysical BS is in the grandparent."

What is this supposed to mean? Clarify please?

Maybe you and Tom are board pals?

[/ QUOTE ]

Actually everything is an unforeseen event in the return of stocks. If you want to say otherwise, either you're wrong, or I want you to PM me which stocks are going to increase in value tomorrow. I'll be happy either way.

The 'metaphysical BS' is just because it has seemed like you're throwing around a few words, but not actually applying them to anything, or maybe even knowing what they mean. What is the process that generates the returns, and what does it look like mathematically? If you're talking about looking at the return of KK versus AA (or any other hand), then I don't think there's anything fractal in there at all. The Law of Large Numbers says that in the long run, the actual probability of a win will approach the theoretical probability. So the graph will have lots of fluctuation on the smaller scales, but none on the larger scales.

Eh, just saw Gonzo's response to you. I'll heed his warning.

But I do enjoy being accused of being 'board pals' with someone when an irrational poster has a couple of people disagree with him. Hilarious stuff.

Bye

Re: Variance is Fractal
 

I think that variance could be a fractal according to the definition of a fractal where a subset would be exhibit the same pattern of the larger set. So you could see small trends exhibit the same patterns as larger trends. That's possible.

But like someone above stated - what does this information, noting the cyclical/wave type of pattern in variance over both small and large sets, do for you? How can we apply this to be useful?

Re: Variance is Fractal
 

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The 'metaphysical BS' is just because it has seemed like you're throwing around a few words, but not actually applying them to anything, or maybe even knowing what they I mean.

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What words am I throwing around sir? And how am I "not applying them to anything"? What is it that you think you get that I do not?

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If you're talking about looking at the return of KK versus AA (or any other hand), then I don't think there's anything fractal in there at all.

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The aa vs kk was merely an example of the mechanical static side of "variance". This "side" assumes mechanical play, preflop to showdown. Like I said you are correct here but refusing to discuss the other 90% of the "game" which is fractal. Understanding this will lead to plugging leaks that you used to blow off as "variance".

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Eh, just saw Gonzo's response to you. I'll heed his warning.

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A "warning" laced of biased perception, ego, hersey! I guess we know why you and him are here.

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But I do enjoy being accused of being 'board pals' with someone when an irrational poster has a couple of people disagree with him. Hilarious stuff

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How can you "disagree" when you are not willing to discuss the relevant issues? Since you are accusing me of being irrational, I'd like you to prove it.

I'll be waiting Shaun.

Re: Variance is Fractal
 

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Eh, just saw Gonzo's response to you. I'll heed his warning.

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A "warning" laced of biased perception, ego, hersey! I guess we know why you and him are here.

[/ QUOTE ]

Actually, my perception is based on what you've written in the threads you've opened. Most of it is so incoherent and nonsensical I can only guess you're writing it high.

Philosophically Speaking, Who Are You, Who Am I, Who Is Who?
WWIII The Setup
Is All Organized Religion Santanic?
Scientiifc Proof of Survival After Death

Re: Variance is Fractal
 

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Eh, just saw Gonzo's response to you. I'll heed his warning.

[/ QUOTE ]

A "warning" laced of biased perception, ego, hersey! I guess we know why you and him are here.

[/ QUOTE ]

Actually, my perception is based on what you've written in the threads you've opened. Most of it is so incoherent and nonsensical I can only guess you're writing it high.

Philosophically Speaking, Who Are You, Who Am I, Who Is Who?
WWIII The Setup
Is All Organized Religion Santanic?
Scientiifc Proof of Survival After Death

[/ QUOTE ]

If the subjects you are referring to are such nonsense why do you freely waste your time opening, reading following and replying? Are you a troll?

I do write like to write when baked. I'd be lying if I said otherwise.

Re: Variance is Fractal
 

[ QUOTE ]
If the subjects you are referring to are such nonsense why do you freely waste your time opening, reading following and replying?

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I didn't reply in your other threads IIRC. I posted in this thread inititally thinking it was legit, then I remembered you. I posted to give the other PT posters a heads up.

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I do write like to write when baked. I'd be lying if I said otherwise.

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No kidding

Re: Variance is Fractal
 

Let's see.. a few definitions for fractal:

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A fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole. Fractals are generally self-similar and independent of scale.

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A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales.

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A geometric pattern that is repeated at ever smaller scales to produce irregular shapes and surfaces that cannot be represented by classical geometry.

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Ok, so you are talking about a concept as though it's a geometric shape. Marijooana is good, mmmm-kay?

Let's list common properties of fractals:

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A fractal often has the following features:

It has a fine structure at arbitrarily small scales.

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Fail, poker actions are discrete.

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It is too irregular to be easily described in traditional Euclidean geometric language.

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Fail, even if I give you the benefit of the doubt translating to a graph, since sample variance is hardly irregular.

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It is self-similar (at least approximately or stochastically).

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Fail, sample variance curves aren't self-similar.

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It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve).

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Fail, obviously.

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It has a simple and recursive definition.

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Fail, obviously.

So I ask again, what the hell are you talking about when you say variance is fractal?

Re: Variance is Fractal
 

Variance is a meaningless term in poker. We talk about variance, but we are all talking about the variances of different things.

Some of us are talking about the variance of luck with the cards - which is actually very low. Some of us are talking about the variance of opponents.

For instance, pretend there is a player who does fairly poorly against 90% of players, but his strategy tends to get huge payoffs against a certain type of player. He will show high "variance." His luck (with the cards) isn't having any variance, what were measuring here is his luck finding suitable opponents.

Add to the fact that opponents adapt to your style over long periods, you have to ask what your trying to measure? Luck, opponents, adaptation of opponents...etc.

Keep in mind that variance is also function of our individual strategies. I can be a very consistent loser if I wanted to be; I am a very consistent winner also when I want to be; but when I try to push my edge...that's often when I experience my so called variance.

I can measure all these things. But when we talk about variance, meaningfully, we need a more precise definition of what we are trying to measure that varies....

P.s. lets stop using hyperbolic words like fractals...and other gibberish... Speak to be understood.

----_Dirty&Litgious_----

Re: Variance is Fractal
 

A small, albet important, reason that higher pp yield more money is because there are less hands that can flop a higher set.

Re: Variance is Fractal
 

[ QUOTE ]
A small, albet important, reason that higher pp yield more money is because there are less hands that can flop a higher set.

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Classic imo

Re: Variance is Fractal
 

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A small, albet important, reason that higher pp yield more money is because there are less hands that can flop a higher set.

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Classic imo

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Wrong thread =(.

So much for my first post here.

Re: Variance is Fractal
 

By claiming variance to not be fractal you are saying the game is purely linear, and non-chaotic? This is obv incorrect.

Chart your poker stats for a few hundred sessions and tell me how fractals appear in charts of something that isn't chaotic and non linear?

Re: Variance is Fractal
 

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By claiming variance to not be fractal you are saying the game is purely linear, and non-chaotic?

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This is obv incorrect.

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Man, you did my work for me.

Re: Variance is Fractal
 

[ QUOTE ]
Let's see.. a few definitions for fractal:
[ QUOTE ]
A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales.

[/ QUOTE ]

[/ QUOTE ]

The OP is, most likely, a loon, but noise (like variance or brownian motion) is self-similar. If you scale up the number of hands you consider at a time, you end up with a different (but similiar) variance.

Re: Variance is Fractal
 

A straight line meets more of the fractal criteria than a variance (deviation from sklanskybux) vs. #hands plot. Weak statistical self-similarity (expected value of point n+x is always the value of point n, for all x.. which is also true for a horizontal line) isn't particularly interesting. If you have a more interesting metric for variance vs. hands that's scale-invariant (and doesn't explicitly use scale in its calculation), I'd be curious.

A 1-d plot of possible deviations from sklanskybux (if the point has been traveresed, it exists), which is just a 1-d random walk, is self-similar because it's just the discrete analogue of a straight line (which is completely uninteresting).

Brownian motion is more interesting because it's 3D, and a random walk in 3D does NOT almost surely cover all points (a 1-D random walk, which variance is, does), so the points covered make a nicely irregular fractal shape.

Re: Variance is Fractal
 

[ QUOTE ]
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A small, albet important, reason that higher pp yield more money is because there are less hands that can flop a higher set.

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Classic imo

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Wrong thread =(.

So much for my first post here.

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ban

Re: Variance is Fractal
 

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Chart your poker stats for a few hundred sessions and tell me how fractals appear in charts of something that isn't chaotic and non linear?

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Re: Variance is Fractal
 

Chaotic != fractal
Fractals are non-linear but not everything non-linear is fractal

It's a common mistake.

Re: Variance is Fractal
 

[ QUOTE ]
Chaotic != fractal
Fractals are non-linear but not everything non-linear is fractal

It's a common mistake.

[/ QUOTE ]

The existence of "fractal waves" in charted poker sessions of any scale are proof of a "chaotic, non linear fractal system at work. This can't be argued.

So I ask then, where do these fractal waves in charted poker sessions come from if they are no part "variance"?

What part of "poker" is fractal if variance is not?

For fractal waves to be observed in charted poker sessions on any time scale (hourly, daily, weekly, monthly, yearly) some part(s) MUST be fractal...

Re: Variance is Fractal
 

Variance vs. hands has no more (and in fact significantly fewer) "fractal" properties than a simple horizontal line. Make a coherent argument (lol, I know) that the "fractal" nature of variance exceeds the fractal nature of a straight line. Hell, for that matter, EXPLAIN what fractal properties variance vs. hands even has, and saying "it's fractal", which appears to be all you can do, isn't an explanation of what fractal properties it has.

Re: Variance is Fractal
 

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The existence of "fractal waves" in charted poker sessions of any scale are proof of a "chaotic, non linear fractal system at work. This can't be argued with me


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FYP

Re: Variance is Fractal
 

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EXPLAIN what fractal properties variance vs. hands even has, and saying "it's fractal", which appears to be all you can do, isn't an explanation of what fractal properties it has.

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"Variance" has many fractal properties such as: repetition of patterns on all scales, infinite detail and complexity, self similarity, recursion...

Re: Variance is Fractal
 

Well, you tried at least. It certainly does not repeat patterns on all scales, since there exist patterns for N hands that CANNOT be duplicated for N/2 hands. It certainly doesn't have infinite detail since it's made up of discrete points- there is no detail beyond the hand/action level. It's only weakly statistically self-similar, as I described earlier, and it's only recursive in the most trivial sum-of-random-sequence way. A straight line is better at all of these properties.

Re: Variance is Fractal
 

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It certainly does not repeat patterns on all scales, since there exist patterns for N hands that CANNOT be duplicated for N/2 hands.

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This is correct assuming "hands" are played correct defined by "the fundamental therom of poker". Of course this is not how we play poker so discussing variance based on "cards" and their distribution is useless. I obviously didn't clarify my ideas into a comprehensible post, which I apologize. Definatly am not the best at getting my ideas out in writing as they are often abstract and non-logical.

I'll try and clarify my points.

Variance is made up of at least 2 main parts. One real (hands/cards) and the other imaginary (our individual "play").

The "variance" you are referring to Tom would represent "real part" of "i" (hands) which could be an integer, fraction, decimal, positive or negative number. Examples are 6, -5, 10.5, 3/4 and so on.

The part of variance I'm talking about is of the "imaginary side" of "i" (-1). Could this not represent our "play" If we let i stand for the square root of -1, ie., i=square root (-1), then any number like 3i, -5i, 1.77i, i/5 is an imaginary number. This being the "chaotic", self similar, recursive and non linear nature of "the game". This area of the game is also infinitively complex and full of detail (infinite and complex styles).

If variance can be expressed as "i", the "real part" would be represented as ("hands") while the "imaginary part" our play. Maybe this imaginary side is what people refer to as "luck" in variance. Luck would then be math as many pros refer to it as...

If true, I have no idea as to how this information could be used to better ones play, other then the awareness of how importance "our play" of the cards is, rather then the cards themselves.

Re: Variance is Fractal
 

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The existence of "fractal waves" in charted poker sessions of any scale are proof of a "chaotic, non linear fractal system at work. This can't be argued with me


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FYP

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I shouldn't have used " cant be argued argued", rather cant be "disproved". I prefer to understand both sides of any "truth", not argue for one or the other. Thanks for bringing that to my attention as I did need to "check myself" on that one. [img]/images/graemlins/grin.gif[/img]

In the middle of "2 opposing truths" is the real truth, or the closest thing to it, so long as we are speaking in quantifiable "S&M terms".

[img]/images/graemlins/smirk.gif[/img]

Of course there is also the "paranormal and metaphysical "truths" " but to a high degree, these tend to corroborate and agree with each other, not oppose like so many Corp. and Gov. funded "orthodoxly studies" of more modern years. So, these truths, do not exist which cuts off the possible read when it comes to incomplete information in any situation or experience and process therein.

Re: Variance is Fractal
 

Paging Tom Cowly, Tom please come to thread "VIF".