Wealth

 

Too Close for Comfort

Be firm, be fair
Be sure, beware
Behave, be there
Be wise, be smart, behave my heart
Don't upset that cat when she's so close

How fair is the distribution of wealth?

1) Brunei; 2) Bahamas; 3) United States; 4) Bahrain; 5) United Arab Emirates; 6) Brazil; 7) Ukraine; 8) Russia; 9) Philippines; 10) Lesotho   This is the list of the top 10 unweighted wealthiest countries per capita in the world in 2021.  This tells you the company that the United States keeps, but it is not weighted by the wealth of the country. Number 1 with a bullet is the United States, which has a weighted ratio of mean per capita wealth to median wealth, weighted by the share of the world’s wealth, of 2.3 while the closest country is China with 0.75. The third place country is Germany with a weighted value of 0.25.  The median per capita wealth in the world is $60 thousand but the mean wealth per capita is $144.9 trillion.  Should we say inequitable distribution of wealth or, it ain't fair.

Kings?

 

If I Were King of the Forest

For courage is the king of kings
With courage I'd be king of kings
The whole year round
I'd be hailed and crowned by every living thing
If I, if I, if I, were K-
King!

Cowardly Lion, you already ARE King of the Forest!

There is a difference between being the Head of State and the Head of Government. Most European Union  and British Commonwealth countries realize this. E.g. Canada and Australia have the British Monarch as their Head of State, not their Head of Government. That is why national highways, parks and museums in Canada were previously  the Queen’s and are currently the King’s.   But the British Monarch is NOT the Head of Government. The death of Queen Elizabeth II was mourned in Canada and Australia, but it did not require a change of government in either of those countries.

In the United States, the de facto Head of State is the President, but the sovereign is The People. The people elect a president but that only makes him head of the executive branch of government, and makes him the representative of the country, but it does not, can not, make him the state.  Unfortunately our current President apparently wanted to be Head of State, but apparently does not want to be Head of Government, a position which he is apparently surrendering to Elon Musk.  It is only custom that the President is the Head of State. Perhaps it is appropriate,  so that the president does NOT get the idea that he is a sovereign,  to explicitly elect or designate a Head of State, which is not the Head of Government.

You can have a good sovereign, e.g. “Good King Wenceslas", or a bad sovereign, e.g. “Ivan the Terrible”, or “Dracula”. The problem is Dracula, Vlad the Impaler, was not viewed as terrible by his own people. Being a sovereign does not make you good. Neither does being the Head of Government make you Head of the State.

The tension between the individual and the group is why there is, and should be, a problem. Being the Head of Government does not mean that you own all of the property of the sovereign. It only means that you are a steward for the sovereign, which according to the US Constitution is The People. Neither does being a member of The People mean that you own all government property.  Being King does not make you a sovereign, any more than Col. Saunders was an army Colonel or Commodore Vanderbilt was a Commodore in the Navy. King is sometimes A sovereign, but in the US is not OUR sovereign. King is merely a name, which is part of your nature.  You can change your name, but that does not change your nature.

Distributions IV

 

Danger Zone

Out along the edges
Always where I burn to be
The further on the edge
The hotter the intensity

Highway to the danger zone
Gonna take it right into the danger zone
Highway to the danger zone
Ride into the danger zone

Is the distribution of wealth in the danger zone?

Wealth is NOT an Absolute zero. It is a Relative zero. As proof take Gershwin’ s I’ve Got Plenty of Nothing from Porgy and Bess. In the song Porgy sings, “ I got my girl, got my song, Got heaven the whole day long, Got my girl, got my love, yes got my song”. If he did not have any of those things, then his nothing would be an Absolute zero. The problem is that in two-dimensional space-time, it is possible to construct an outcome matrix which is absolutely TRUE,  
{2/3, 0, 1/6, 1/6} .  This matrix satisfies the components of {true win, true loss, false win, and false loss} and is 100% certain.  It is also possible to construct another outcome matrix which is absolutely TRUE. {3/3, 0, 0, 0} .  The problem is that an absolute matrix can also be constructed which is {1/3, 0, 1/3, 1/3} which is absolutely FALSE and is 100% certain. ( This also suggests that an absolute has three aspects, is a trinity)

Individuals can form a group to act like an absolute. In two dimensional space-time their outcome can be {66.7%, 0, 16.7%, 16.7%}, which is also absolutely TRUE. That normal distribution of individuals can also be skewed maximally positive to {96%, 0, 2%, 2%} which is close to being absolutely TRUE. But that distribution can also be {46.3%, 0, 26.85%, 26.85%} which is skewed maximally negative, and is absolutely FALSE. The problem is that normal individuals acting as a group can not perceive the absolute. They can only perceive at most 5/6^th of the absolute. The danger zone is any outcome, distribution, between {50%, 0, 25%, 25%] and {65.9%, 0, 17.05% 17.05%}. It might appear to be true, but this may be an illusion because the absolute might be perceived incorrectly. The problem is that these appear to be “winning” distributions in that the sum of True wins and False wins is greater than False losses,  but the distribution of wealth is already in the danger zone and the variance in that distribution of wealth is increasing.

Bullies

 

Do You Want To Know A Secret?

Listen
Do you want to know a secret?
Do you promise not to tell?
Whoa, oh, oh

Your votes should be secret!

Retaliation is the crime of acting against an individual for actions taken in that individual’s own best interests. Intimidation is the crime which involves defettering or coercing an individual to act against their own interests. There is only a difference in time between the acts.   Retaliation is about past acts, intimidation is about future acts. Both are forms of bullying, which includes both of these acts, as well as present acts. All need fear, domination. "Hold tight to  your anger. Don’t give into your fears. Take your best shot let me see what you’ve got. Bring on your wrecking ball."

But that requires the courage to take a bully’s best shot. If those actions are in secret, then there is no need to fear a bully’s wrecking ball. That is if your votes are secret. Then there is nothing to fear except fear itself to coin a phrase. Don’t be bullied. Keep your vote secret.  It is your own interest that should guide you, not the interests of a bully. They can try to persuade you, but that does NOT include forcing you.

Nothing

 

Something Good

Nothing comes from nothing
Nothing ever could
So somewhere in my youth or childhood
I must have done something good

What kind of nothing?

One of the great errors is assuming that there is only one kind of zero, nothing. There are actually three kinds of zero. 1)Absolute zero 2) Relative zero and 3) Repeating or cyclic zero.

1.      Absolute zero is defined as the value below which there can be no observations; x>0; 

2.      Relative zero is a zero relative to absolute zero that is inserted for the convenience of recording the observations of the value. Thus while it is possible to talk about -4000 degrees Fahrenheit, in fact no temperature is defined, possible, below -459.67º F, which in this case sets a lower limit for the location parameter; μ; x>μ

3.      Repeating or cyclic zero is a recognition that a wave may pass through the x-axis and appear to be zero on a periodic, p,  basis: even when x is infinite and n approaches infinity;  n*p>x>(n-1)*p.

Given that there are four quadrants formed  by two dimensions, (e. g. winning and losing,  true and false, etc.), when one of those quadrants is absolute, then the other three quadrants must be one of the three zeros for the outcome in the total of those quadrants to be absolutely certain, 100%. This means that there are 4 quadrants in which the absolute can be placed as long as there are zeros in the remaining quadrants. Hower imposing the additional criteria that the absolute has to be true AND a winner, means that only one of those four solutions is real. For any number of players greater than 3, an outcome ensuring a certain winner is true is always possible,

When there are only two dimensions, e.g. players, for example space and time, then the surface passing through those two dimensions can be flat, hyperbolic or spherical. If the surface is flat or spherical, then there is only one solution. If the surface is hyperbolic, then  there are two solutions. But there are three outcomes to a contest: win, lose AND Tie. If an additional criteria is imposed, then it is possible to find a solution which is winning and true by also requiring that false wins and false losses be equal, and whose total is a tie. Thus it is possible to accommodate 3 outcomes among the two dimensions AND the surface. A solution matrix, table, which is winning, true AND normal is {2/3, 0, 1/6, 1/6} which satisfies {true win, true loss, false win, and false loss}. This is true for the absolute. However an observer who is not an absolute will only perceive 5/6, or 1/6, of the absolute, depending on which side of the hyperbolic surface that observer is located. In that case the solution can only be at maximum√ (5/6), or 91.3%, certain, not 100% certain. Another solution can be certain, but then that solution also must not be true.

There is an additional proof that the surface connecting the 2 dimensions is hyperbolic, in order to be absolute and true. An absolute has no error and there is nowhere the absolute is not, i.e. 0, and its error is 0,  Since waves on a surface will interfere with each other, the first part of the statement can be satisfied if μ≥0 and the second part of the statement satisfies σ/√∞ which is true if σ=0 OR if σ is any constant greater than 0.  A hyperbolic surface will accommodate 2 solutions. A group of individuals on a hyperbolic surface may perceive the absolute as an infinite series of trigonometric waves. If that is the case the μ=0±σ=0 is true, but is a solution which only applies to the absolute . The solution must always be always applicable, that is any value of μ and a constant value of σ. Since the definition of a wave is that σ²=½A² and that wave  has a period of 2π in the case of most trigonometric waves or 2πi for most hyperbolic trigonometric waves, for a normal solution σ²=s²π²/3, then the solution which results is a constant (e.g., winning or losing,  true or false, etc.) is π/6 .  This satisfies the requirement that there be two solutions on a hyperbolic surface, σ=absolute zero AND σ= π/6.

This also mean that the multiplicative and additive identities for zero only applies to only ONE of the three zeroes, the Absolute Zero.  Those laws do NOT apply to Relative or Repeating zeroes. Choose your zero, nothing, wisely.

Variance II

 

Ain’t We Got Fun

There's nothing surer
The rich get rich and the poor get poorer
In the meantime, in between time
Ain't we got fun?

Do the rich have to get richer, and the poor get poorer?

Given my recent blog post that variance ( e.g. the difference between rich and poor) should be a constant, https://dbeagan.blogspot.com/2025/02/variance.html. it is appropriate to review an earlier blog post on the difference in wealth among nations.  https://dbeagan.blogspot.com/2021/11/distribution-of-wealth-iii.html .  As well as a blog  on the consequences of keeping the location parameter constant and allowing the variance to increase to accommodate growth.  https://dbeagan.blogspot.com/2023/09/distribution-of-income-ii.html

The fact that variance is a constant and location is not, can lead to bad policy decisions if it is wrongly assumed that location is constant and variance is not.  It is totally correct that things were better from 1946 to 1964, and that things were much worse from 1996 to 2013, just as it is true that Christmas is better than the Dog Days of Summer.  But making every day Christmas is a stupid and childish response, just as MAGA is.  The grown‑up response is to work hard during the Dog Days of Summer so that the following Christmas can be as good, or even better than, the past Christmases that you do remember.  The fact that humans don’t live through more than portion of two cycles of historical periods of 100 years does not mean that the cycle is not there, just that a single individual can not experience multiple cycles. 

Mark Twain said that “History doesn't repeat itself, but it often rhymes.”  William Faulkner said that the “The past is never dead. It's not even past”.  Just because you can’t see other cycles, does not mean that other cycles do not exist, only that you can’t personally experience them. Learn from a study of the historical past.  Grow up! It can’t be Christmas every day!  Don’t be a such a child!

Surfaces

 

Blue Horizon

Beyond the blue horizon
Waits a beautiful day
Goodbye to things that bore me
Joy is waiting for me
I see a new horizon
My life has only begun
Beyond the blue horizon lies a rising sun

The horizon is why Pythagoras Theorem applies Locally by not Globally

There are three kinds of surfaces. 1) Spherical, 2) Flat (Euclidean) and 3) Hyperbolic. While it seems like we live on a flat Earth, the existence of the horizon is actually one of the proofs that the surface of the Earth is actually a sphere, not flat. An observer can perceive 50% of any object that is between the observer and the horizon. An observer can not perceive the object at all if it does not extend above the horizon. However the observer can only perceive 50% of the portion of any object that extends above the horizon. That is why the mast of a sailing ship on the horizon is visible before the rest of the ship, because at that point  the mast extends above the horizon, but the rest of the ship does not. The horizon is defined by the radius of the spherical surface. If the sphere is large enough, then most objects which are perceived will be between the observer and the horizon. But that does not mean that the horizon does not exist, just that it is not always perceived. A Flat surface is thus only the limit of the spherical domain, not a domain itself. The surface will have a curvature defined by the major and minor axes, a and b, of the equations describing the eccentricity of the surface. If a and b are both less than infinity, then a spherical surface is described, and the eccentricity is less than 1. If a and b are both infinite, then a hyperbolic surface is described, and the eccentricity is greater than 1. A flat surface is thus only the boundary between these two conditions where the eccentricity is exactly equal to 1.

For any hyperbolic surface, regardless of the curvature, only 5/6 or 1/6 of an object will be perceived, depending on which side of the hyperbolic surface is being perceived by an observer. That is because a hyperbola has two solutions, one which is the opposite sign of the other. But the solutions are similar to the spherical solution until the numbers involved are very large: e.g. 2/3 the size of the universe or 5/6 the speed of light. Thus could it  also be said that the universe is flat locally, but hyperbolic universally.

Variance I

 

Too Much of Nothing

Too much of nothin' can turn a man into a liar
It can cause some man to sleep on nails
Another man to eat fire
Everybody's doin' somethin', I heard it in a dream
But when it's too much of nothin', it just makes a fella mean
Say hello to Valerie, say hello to Marion
Send them all my salary on the waters of oblivion 

Say hello to Variance too! 

A normal random distribution is defined by its location, often called the Mean/Median/Mode, μ,  and its Variance, σ². The mean/median/mode are not equal, except at infinity. The mean, often called the average, is computed from the total of the observations divided by the number of observations. The variance is the range of the observations but is not as easy to compute. An observation consists of where you are observing a thing,  its x value, and what is the attribute of the thing that you are observing, its f(x). Just because the x-axis is infinite it does NOT mean that the function on that x-axis is also infinite. For example, a wave is a repeating function, f(x)= cos(x). In this case x can be any number, e.g., infinity, ∞, but the value of f(x) can only be between -1 and 1. Mathematically this would be stated that the domain is infinite, but the range is finite and between -1 and 1.  The variance, the range, can be finite even if the input variable, the domain. is infinite.

It is fairly easy to compute the mean of a variable. It is the total of all of the observations divided by the number of the observations. It is a little harder to compute the variance of the observations, but not impossible. If an infinite number of variables is computed then the mean by definition is half of infinity. But it is important to differentiate between infinite variables and infinite domains. Just because the domain is infinite that does not imply that the mean/median/mode is infinite or that the variance is infinite. These are characteristics are of the range, not the domain. The range can be finite even if the domain is infinite, for example, the cosine (x). The mean/median/mode of the cos(x) is sine (x). The variance of the cosine, and the variance of the sine for that matter which is also the mean/median/mode of the cosine, is ½.

The variance is thus a constant. The variance of the range is always a constant, even  if the domain is infinite. Thus it is not inconsistent to say that the variance of infinity is a finite number. The mean of cos(x) is sin(x) whose domain is also infinite, but the variance of that cosine function, and its mean the sine, is, ½,  which is finite.

Cycles

 

It’s Still Rock and Roll to Me

Don't waste your money on a new set of speakers
You get more mileage from a cheap pair of sneakers
Next Phase, New Wave, Dance craze, anyways
It's still Rock and Roll to me

And it’s still Mathematics to me!

I believe that there are historical cycles of  approximately 100 years. I say approximately, because the length of the historical cycle is a random phenomena whose average is 90 ±10 years. Half of a full period of a cycle is thus 45±5 years and 1/6 of a half cycle would thus be on average 8 1/3 years long. If the last Turning (end of a cycle) was in October of 1929, then you would expect an upward slope from approximately 1929 to 1979. And  a downward slope from approximately 1979 to 2029. In the first 1/6 of the first half cycle, e.g. ~1929 to 1938,  there would be slow to virtually no growth and that growth may be virtually indistinguishable from the decline at end of the last cycle. To an observer in the midst of a cycle, it may appear as if the cycle ended sometime in the middle of that period, e.g. 1932 ( i.e. it appears like a lag variable). 

There should be moderate growth for the next 1/6 of the half cycle (~1938 to 1947). There would be twice the rate of growth for the next 1/6 of a half cycle ( ~1947 to 1956) and that rate of growth would be accelerating. There would be almost the same rate of growth during the next 1/6 of the half cycle (~1956 to 1964), but that growth would be decelerating. During the first 1/6 of the next half cycle the growth is declining but the change is virtually indistinguishable from the last 1/6 of the previous half cycle. The rate of decline accelerates during the next 1/6 of a cycle, (~ 1979-1986). The rate of decline virtually doubles during the next 1/6 of the cycle, ( ~1986-2004). The highest rate of decline happens during the next 1/3 of a half cycle, (~2004 to 2020). The rate of decline decelerates during the next 1/6 of the half cycle, (~ 2020-2029). The last phase of the cycle has virtually no growth, just like the first 1/6 of the next half cycle where growth returns.

Yes, the length of each phase can vary. Wars, economic downturns, terrorist attacks, extreme weather  and other random events can occur. What about on average is so hard to understand?

There is a danger zone about 80% through a declining half cycle where things may have gotten so inequitable that revolution against the sovereign can happen. That puts the danger zone at somewhere between 2020 and 2029 where there is a strong possibility that the subjects of the sovereign will say off with their heads.

Standard Deviation

 

A.D.H.D.

Fuck that, eight doobies to the face
Fuck that, twelve bottles in the case nigga. Fuck that
Two pills and a half, wait nigga, fuck that.
Got a high tolerance when your age don't exist

And tolerance is where it’s at!

I would be lying if I said I understood anything that Kendrik Lamar said during the Super Bowl LIX halftime show. I don’t speak Rap. But Kendrick’s lyrics as quoted above are wise beyond words, The language is very rough, but….maybe I am merely showing my age. Tolerance is what engineers call Standard Deviation, the square root of variance. A problem is acting like mean and the midpoint of tolerance squared, variance, are the same. They are NOT, except for the absolute. There are three outcomes to any contest: win, lose, and tie. There is an average, mean of that contest. The average plus the tolerance should include the entirety. But because the mean, average, is defined as half of the absolute, it is confused that this requires that mean be constant, when it is NOT or the tolerance to be NOT constant, when it is. One is subject to growth, the average, and one is NOT subject to growth, the tolerance.

According to L’Hôpital’s rule, the limit of the average is the mean AND the median. But for anything less than the absolute, the mean and median can, and will, be different. The mean of an even number is half of that even number. The mean of an odd number is NOT an odd number, it is half of the original number, which makes it an even number. Thus saying the variance is one third of the absolute, while the location, is half of the absolute seems like it is a contradiction but the mean is subject to growth, and the variance is a constant and is NOT subject to growth.

Mathematically x>μ AND σ=μ/3 is true for the absolute but that does not mean that variance increases as the mean, location, increases. The variance is a constant, but the location can change with growth. The problem is that the limit of N/2, the mean, as N approaches the absolute is the absolute , but the limit of the Standard Error, what engineers call tolerance, the square root of the variance is SE=σ/√N, zero. This is true if the absolute is zero, but it is also true if the absolute is NOT zero, x>μ and σ=μ/3 is true not only for N=0, but it also is true for any value of the number N. There is no contradiction,  The mean is a function and changes. The tolerance is a constant and can NOT change. And apparently by not growing up in Compton like Lamar, I missed that.

Atheists

 

Universal Soldier

He's a Catholic, a Hindu, an Atheist, a Jain,
A Buddhist and a Baptist and a Jew.
And he knows he shouldn't kill,
And he knows he always will,
Kill you for me my friend and me for you.

Not only are Scientists NOT Atheists, but Evangelicals must be Pro-Choice!

Just because the words are different doesn’t mean that it is not the same concept. Scientists say that they are Atheists but they probably also believe in infinity, an absolute. Those are the same thing, just using different words. Not only do scientists believe in an absolute, but they also believe in only one absolute.

Scientists believe in space-time. Space, x,  has an absolute: that is x>0. Time, t,  is related to space by the constant speed of light: c=∆x/∆t .  Speed is always defined as the change in space divided by the change in time. If the speed of light is a constant, then an absolute in space is the same absolute in time. But there is an infinite amount of time, before the time which is Now, and an infinite amount of time after Now. Thus Now is a relative zero but the absolute, infinity, is the same based on the constant speed of light. If space is absolute, and time is based on the same absolute, then there is only one absolute: a “mono” absolute. If you say absolute or theist, then you are effectively saying the same thing.

If time is a relative zero and space is an absolute zero, then scientists and all theists must also believe in choice. The future is merely all choices. The past is only the choices which have been made, but the amount of those choices in the past are the same as in the future. Thus saying that you believe in a future means that you believe in choices. So not only are scientists NOT Atheists but Evangelicals must be Pro-choice if they are not Atheists.

Rules

One, Two, Three

One, two, three
Oh, that's how elementary
It's gonna be
Come on let's fall in love
It's easy
Like taking candy
From a baby.

THREE is not only elementary, but it's also fundamental.

The ancient East Asian painting of the Three Vinegar tasters is supposed to be a representation of 1) Confucius, (Kung Fu Tse); 2) Lord Buddha; and 3) Lao Tse (the founder of Taoism) tasting vinegar from the same jar.

1. Confucius says that the vinegar tastes bitter which demonstrates to him that rules are necessary to impose order over chaos in reality and that it is up to you to impose that order.
2. Lord Buddha says that the vinegar tastes sour which demonstrates to him that all reality has to be endured so that you can pass from reality to the unobserved.
3. Lao Tse says that the vinegar tastes just like it is supposed to taste in reality. There is both reality, the observed, and the unobserved, but they are different to him.

Of the three, I’m on Team Tao. The fact that reality, the observed, is different than the unobserved does NOT mean that one or the other is better, only that they are different. Vinegar tastes how it is supposed to taste in reality, but that doesn’t mean it won’t taste differently in some place other than reality. What is “order” in reality,  might be considered “chaos” in the unobserved.

Common Sense.

 

Common As Muck

You're not Bridget Bardot, I'm not Jack Palance.
I'm not Shirley Temple by any circumstance,
Or Fred Astaire

We're as common as muck.
Bonne chance, viel glück, good luck
Where bold is beautiful, we don't give a damn
Luvva duck, we're as common as muck.

Maybe common sense isn’t very common.

We assume our leaders will have common sense. Leaders on average do approximate the range variable, s,  the tolerance, aka the Standard Deviation, of the absolute. In fact they match it better than most other ages of life in a group. But those who should be leaders are only 60% of the group.  The Voters and Advisors do better at matching the Absolute.

Even leaders can’t perceive the location variable, μ, of the absolute. They pale besides the Nash Equilibrium, whose followers perceive more of the absolute than is actually there. A Nash Equilibrium acts like the Absolute has a median/mean/location that is 120% of its actual value. But by doing so, it ensures that the members of the group are closer to their perception of the absolute.

		s	μ	Absolute Zero	100%	Absolute
Perceived	Young Ward	0.070	NA		0.45	41%
	Voter	0.288	NA	0.041	0.86	90%
	Leader	0.459	NA	(0.042)	1.22	144%
	Advisor	0.288	NA	(0.221)	1.04	90%
	Old Ward	0.070	NA	0.142	0.96	41%
	User Optimal	NA	0.000	1.500	NA	NA
	System Optimal	0.250	NA	0.500	2.91	100%
	Nash Equilibrium	0.500	1.885	0.023	2.91	100%
Absolute		0.500	1.571	0.000	3.142	100%

 

Individuals acting as a group perceive the absolute from their own frame of reference, hyperspace. By acting as if the Absolute is more than what can be perceived, the group can better match their perception of absolute.

But the values in the table for leaders are only the average of all those who could be leaders, not those individuals who are actually chosen as leaders. Individuals within the group of leaders are just as subject to error as anyone else. And even leaders are better at only the range of the absolute, not the Absolute itself. The current allies in MAGA of User Optimalists and System Optimalists don’t come close to the  the Absolute.  That is reserved for Nash Equilibriumists.  Even the common sense of leaders is NOT very common, and it definitely is not absolute.

Discontinuity III

 

Crossroads

I went down to the crossroads
Fell down on my knees
Down to the crossroads
Fell down on my knees
Asked the Lord above for mercy
Take me, if you please

A discontinuity is a crossroads

In a speed-volume curve of traffic or water flow, there is a discontinuity at which laminar/uncongested/orderly flow becomes turbulent/congested/chaotic flow. At this discontinuity there is a crossroads in the behavior of the flow before the discontinuity and the behavior of the flow after the discontinuity. The flow approaches the crossroads/discontinuity from reality, from Point D in the figure below.

At the discontinuity, Point E, it can remain in reality on the left side of the figure, and move to the curve connecting Point A with Point E, from the orange curve to the blue curve. However that requires a rotation by 3/2 π  and this requires that the equation describing the flow from Point D to E to become the logarithm of a negative number, and that behavior is undefined. It can move to the curve connecting Point E to Point at C, also moving from the orange curve to the blue curve, a mirror of the original behavior, but that requires moving the wrong way on a one-way link. It can move to the curve connecting point E with Point B and stay on the orange curve. That is a continuation of the original path, but it requires moving to the right side of the figure, which is NOT observable reality. It is unobservable behavior. At the crossroads any of those behaviors is possible, but each has problems. But moving from reality to unobservable flow seems more likely at the crossroads than any of the other possibilities.