Friday, December 8, 2023

Sanctions

 

Gimme Shelter

Rape, murder, it's just a shot away
It's just a shot away
Mmm, a flood is threatening
My very life today
Gimme, gimme shelter
Or I'm gonna fade away 

Making something against the law doesn’t eliminate it.

There is an international convention against genocide, therefore there should be no genocide, correct?  There are sanctions in place against Russia’s invasion of Ukraine, but since there is still fighting, therefore sanctions don’t work, correct?

If you believe these, then you must also believe that rape and murder, which I believe are also against the law,  never occur.  The law can only deter actions, not prevent them. Sanctions are put in place to punish actions, but also to make sure that you are not an accessory to, complicit in, those actions.  Laws and sanctions can signal society’s disapproval. Laws against rape, murder, or genocide are not invalidated by an illegal act.  They are meant to signal society’s position and to deter such actions. They should be judged by the actions that might otherwise have occurred,  not on those actions, which despite the laws and sanctions, did occur. Bad things are still just a shot away.

Uncertainty

 

Them There Eyes

I fell in love with you the first time I looked into them there eyes
And you have a certain lil cute way of flirtin' with them there eyes
They make me feel so happy, they make me feel so blue
I'm fallin', no stallin' in a great big way for you

Maybe them there eyes are not so certain after all!

Arguing that 3+3 ≠6 is madness.  But arguing that √32≠3 may NOT be madness. 

The reason is that 3=√32 is true only for a flat, Euclidean, surface.  The formula for a hyperbolic surface would be 3=ln(cosh(3)±sinh(3)).  This has the value 0±6.

In fact for the first ten integers, the uncertainty term is as given in the table below.

x

Flat, Euclidean surface
√x2

Hyperbolic surface
ln(cosh(x)±sinh(x))

1

1

  0±2

2

2

  0±4

3

3

  0±6

4

4

  0±8

5

5

  0±10

6

6

  0±12

7

7

  0±14

8

8

  0±16

9

9

  0±18

10

10

  0±20

There is a pattern here.  For n, on a hyperbolic surface, the solution is 0±2*n.  This suggests that there is a non-zero uncertainty that increases as n increases.  And since there is uncertainty, then our universe may be hyperbolic.  There is a reason why we don't notice this uncertainty.  It is because we measure x in units other than the absolute.  If the absolute is π, then numbers greater than the absolute,  approximately 3.14, are meaningless.  In fact the distances which are regularly encountered are mere fractions of the absolute which means that the uncertainty regularly encountered will also be mere fractions of the absolute. Additionally while the uncertainty suggests that negative numbers are allowed, in fact in reality, if we are measuring x on an abolute scale, negative numebrs are not allowed and rather than the total value with uncertainty, a more useful concept might be the most probable postive number.

Thursday, December 7, 2023

Variance III

 

Casey Jones

Driving that train, high on cocaine Casey Jones, you'd better watch your speed Trouble ahead, trouble behind And you know that notion just crossed my mind

What if we are high on something other than cocaine?

The movie The Seven Percent Solution dealt with Sherlock Holmes addiction to a solution of seven percent cocaine.  The variance, σ2, of the universe with a mean choice of 0.5 appears to be 0.822467. But this is a complex number that is really 0.822467 + 0*i.  The zero coefficient of the imaginary axis means that it is zero, not that the imaginary axis does not exist. 

The solution for the Standard Deviation, σ, the square root of the variance, depends on whether it is solved on a flat, Euclidean, or on a hyperbolic surface.  On a flat surface, the Standard Deviation would appear to be 0.9069, which is 2.9% higher than the solution of  0.8807 on a hyperbolic surface.  Should we deal with our belief, addiction, that we live on a flat surface and admit that we might intead live in a hyperbolic universe?

Wednesday, December 6, 2023

Death

 

And When I Die

And when I die and when I'm gone There'll be one child born In this world, carry on, to carry on

We all die, but the world carries on

·        Norman Lear, 101, American screenwriter and producer

·        Sandra Day O'Connor, 93, Associate Justice of the Supreme Court

·        Henry Kissinger, 100, German-born American diplomat and politician.

·        Rosalynn Carter, 96, First lady of the United States

·        Maryanne Trump Barry, 86, Judge and sister of Donald J. Trump.

·        Frank Borman, 95, Astronaut.

·        Bob Knight, 83, Hall of Fame basketball coach

In recent weeks, obituary writers have been kept busy by the deaths of many notable Americans.  The partial list above of the most famous people shows the good and bad, who have died mostly at very old ages.  “The evil that men do lives after them; The good is oft interred with their bones.”  They, and we all eventually, will be interred. But there will be a world that remembers us.  The individual eventually dies, but the group lives.  Is this a lesson that the group is more important than the individual?  Carry on.

Tuesday, December 5, 2023

Parabolas

 

She’s Like A Rainbow

She's like a rainbow Coming, colours in the air Oh, everywhere She comes in colours

Rainbows are pretty, but they are illusions.

To paraphrase Lady MacBeth, out damned parabola, out I say.

There are two forms of growth: geometric, also known as parabolic, and exponential. In geometric growth the assumption is that the rate of increase is continuous AND constant. This means that in the presence of a limit to growth, that eventually the growth will exceed that limit and the growth will become imaginary. By contrast exponential growth is continuous but NOT constant. It will approach the limit but will not exceed it and will never become imaginary.

A parabola is the midpoint between an ellipse (a circle is a perfect ellipse) that has an eccentricity less than 1, and a hyperbola that has an eccentricity greater than 1. A parabola is a formula/curve with an eccentricity exactly equal to one. However I would suggest that it is metastable to be exact, and the universe is thus proabaly stably hyperbolic as proposed by Mabkhout (Mabkhout, 2012). This may mean that parabolas, Gravity’s Rainbow, and gravity itself, are illusions. They are useful illusions, but illusions, nonetheless.

Just as there are those individuals that believe in a Flat Earth, because Pythagoras’ Theorem which only applies on a flat surface, gives good results, compared to the correct spherical formula. (Actually those individuals probably do not even know that there is a Pythagoras’ Theorem!). The reason it gives good results is that when the spherical surface is very large, compared to the values in Pythagoras’ formula, then there is an imperceptible difference between a flat and spherical surface. However commercial airplane pilots will tell you that you that the Great Circle Distance is much more useful than Pythagoras’ formula over distances between continents.

Similarly Newton proposed a Law of Gravity. (An aside. It is only called a Law because of the History of Science. Today it would be called a Theory). Newton was proven incomplete by Einstein. Newton’s Law assumes a constant mass, and Einstein’s Theory shows that the relative mass of an object increases as that object approaches the speed of light.  But when an object is moving at very low speeds compared to the speed of light, there is virtually no difference between Newton’s Law and Einstein’s Theory. But Einstein’s Theory was still applied in a flat universe and therein lies the rub. In a non-flat universe, the increase in relative mass might not follow Lorentz’s adjustment, but the difference might be imperceptible at the speeds commonly encountered.

However if the universe has a hyperbolic shape, then gravity itself might be an illusion where two or more objects approach a common center on that curved, hyperbolic, surface. In this case, just as Einstein’s Theory is more correct than Newton’s Law, Newton’s Law continues to be used because it is simpler to apply, even if Gravity is an illusion, Newton’s Law and Einstein’s Theory might be “wrong” but in the words of George Box, they might be useful.

If the universe has an absolute, then the distribution of objects in that universe can be expected to follow a distribution within that absolute. For an arbitrary absolute, for example π, objects within that absolute should be expected to follow a random distribution. One such normal random distribution is the logistics, also known as the hyperbolic secant squared, distribution, whose Probability Density Function, PDF, is (1/(4*s))*sech2((x‑µ)/(2*s)), where s and µ are parameters of that distribution. Its Cumulative Distribution Function, CDF, is also a hyperbolic trigonometric function, ½*tanh((x‑µ)/(2*s))+½. If objects are uniformly distributed, then the mean, and the median, of that normal logistics distribution, µ, is at half of the absolute, or in this example, π/2. When x is at that mean, median, there should be 50% of all objects, a PDF of 0.5, which requires that in this example s=0.5. Its variance, σ2, is s2π2/3 or 0.822.

Another normal distribution is the Gaussian distribution. Its Probability Density Function, PDF, is 1/(σ*√(2*π))*e(-0.5*((x-µ)/σ)^2), where its parameters are σ and µ. Its Cumulative Distribution Function, CDF, is 0.5*(1+ERF((x-µ)/(σ*√(2)))), where ERF is the standard error function.  As shown in the figure below when the PDF of the normal logistics function at the mean, median is 0.5, the PDF of the Gaussian is 0.44.  If the PDF of the Gaussian is 0.5 at the mean, median, then the s parameter of the logistics distribution must instead be 0.44 and its PDF is then 0.57 instead of 0.5.  Neither the logistics nor the Gaussian distribution are zero at value of x of zero or the absolute. The Gaussian distribution on a flat surface has almost the same values as the Gaussian distribution on a hyperbolic surface. 


Also shown in that figure is a parabola with a coefficient of 1 which has a value of 0 at an x of 0.  This does NOT have a value of 50% at the median, mean, µ.  In fact it becomes very large near the absolute.  A parabola can be made to take on a value of 50% at the median.  The reflection of the adjusted parabola, which creates a discontinuity, can be used at the mean, median. This will result in a value of zero at the absolute.  However a parabola and its reflection is not as simple as a logistics distribution. A logistics distribution is also smooth and does not create a discontinuity at the mean, median. However using a simple parabola can highlight how the integral of the PDF, the CDF can be viewed.


The CDF, integral or area under the curve, of the PDF of a simple parabola is identical to the formula for the area of a triangle.   However, as shown, it has a height of 1.57, π/2,  rather than a height of 1 at the absolute, if the absolute is assumed in this example to be π, which should be the CDF and is approximately the value of the CDF of the normal logistics distribution on all surfaces and the normal Gaussian distribution on a flat or hyperbolic surface. However if the CDF of a parabola, the formula for the area of a triangle, is translatedon the y axis, reduced, by a value of .29, it becomes almost identical to the CDF of the normal distributions near the mean, median.  It continues to approximate the CDF of the normal distributions up to a distance of π/6 from the mean, median, of π/2.  At this distance the slope changes to become approximately half of the previous slope and this continues for a distance of π/6 from the last change.  At this point, the slope again changes to become approximately half of the previous slope. This continues to an x of the absolute and an x of zero, the absence of the absolute. 

The fact that the formula for the hypotenuse of a triangle on a flat surface must be adjusted suggests that the correct formula should not be on a flat, surface.  The logistic distribution is consistent with, and uses, hyperbolic trigonometric functions.  It has parameters of s=0.5 and µ=the absolute divided by 2.  It is observed that an s of 0.5 is also consistent with the mean of a single choice of that absolute.  It is also suggests that the Gaussian distribution was an attempt to derive a normal distribution on a flat surface, when it should have been derived for a hyperbolic surface.  It is also observed that the 68/95/99 rule of a Gaussian distribution on a flat surface corresponds to a 52/85/100 rule for a logistics distribution on the  hyperbolic surface of the universe ( 52% percent of the values fall within ±1/3 of the mean, median; 85% of the values fall within ± 2/3 of the mean,median; and 100% of the values fall within ± 3/3 of the mean, median.  Rather than an arbitrary variance, when the choice parameter, s, is equal to 0.5, the variance, σ2, has a fixed value of 0.822467 and the square root of the variance, also known as the Standard Deviation, has a fixed value of 0.9069.  

The 68/95/99 rule is for the multiples of the standard deviation of a Guassian distribution on a flat surface.  For a logistics distribution on a hyperbolic surface, when 100% of the values fit within the range of the absolute, 

  • 70.6% are within the mean, median, ±  σ; 
  • 94.3% are within the mean, median, ±2σ; and 
  • 99.0% are within the mean, median, ±3σ.

It is suggested that the surface of the universe is hyperbolic.  It is suggested that the distribution of objects follows a logistics distribution.  It is suggested the parameters s, variance, and standard deviation must all take on nonzero values in reality.  

At the mean, median, the dominance is 100% and it remains this value for any outcome.  However 

  • at the mean, median, ± 0/3 of the mean, median, there is  25% certainty; 
  • at the mean, median, ± 1/3 of the mean, median, there is  52% certainty; 
  • at the mean, median, ± 2/3 of the mean, median, there is  85% certainty; and 
  • at the mean, median, ± 3/3 of the mean, median, there is 100% certainty.  

If the distances commonly encountered are less than 1/3 of the range of the absolute, then there is no appreciable difference between the results for a flat or hyperbolic surface.

Parabolas may be an illusion.  We may aspire to live on circles.  But we appear to live on a hyperbola.

Mabkhout, S. (2012). The infinite distance horizon and the hyperbolic inflation in the hyperbolic universe. Phys. Essays, 25(1), p.112.

 

 


 



Sunday, December 3, 2023

Dimensions

Medley: Aquarius/Let the Sunshine In (The Flesh Failures)

Now let me tell you one thing (let the sunshine) I want you to sing along with The 5th Dimension (let the sunshine in) Hey, open up your heart (the sunshine in) Come on! (let the sunshine) And let it shine every day (let the sunshine in)

So how many dimensions are there?

The song above was a Grammy Record of the Year for the Fifth Dimension in 1970 .  Are there five dimensions? There are the three dimensions of space, x, y, z also known as length, width and depth. There is the dimension of time.  If we add the dimension of the imagination then there are five dimensions. If reality is defined as space and time and zero imagination, that zero is only the coefficient of the axis, dimension, of  imagination and there are thus five dimensions of reality.  So the name of the singing group is more than appropriate.  Let the Sunshine In!


Saturday, December 2, 2023

Show Your Work

 

Show Me

Sing me no song! Read me no rhyme!
Don't waste my time, Show me!
Don't talk of June, Don't talk of fall!
Don't talk at all! Show me!

Show your work!

The formulae shown in red in this post have been corrected.

When I was in college, I was famous for submitting tests with minus the correct answer or with some other simple mistake.  On numerous tests, I was saved by the fact that my instructors took pity on me and gave me credit for showing my work.  Ironically, I now find myself with what appears to be the correct answer for a hypotenuse on a hyperbolic surface, but because I did not save my work, I can not prove it.

On a flat surface the hypotenuse/radius of a triangle is r=√(a2+b2).  I would like to say that on a hyperbolic surface this is r=ln(0±2*cosh(√(a2+b2))), which I arrived as a solution and it seems to work, but I did not save my work.  Thus because I did not save my work, I am unable to prove that on a hyperbolic surface it is r=ln(0± 2*cosh(√(a2+b2))), instead of r=√(a2+b2). Being unable to show my work means that I am unable to prove this equation and unable to show that:

The Lorentz transform, which is typically given as√(1-(v/c)2), where in this case v is the velocity of an object and c is the speed of light, should instead be r=ln(0±2*cosh(√(1-(v/c)2))).

In a curved universe, gravity should be an apparent force and should NOT be combined with the three intrinsic (electric, weak nuclear, and strong nuclear) forces in a Unified Field Theory.

In a hyperbolic universe, there is a discontinuity at the Big Bang and our universe may be only one sheet of a asymmetrical two-sheeted  hyperboloid.

In a hyperbolic universe, there is only one absolute, and that absolute is both random AND deterministic.

If there is one absolute, then there is also only one choice: choosing that absolute, and not choosing that absolute, aka absolute zero. 

In a hyperbolic universe, regressions and statistics using least squares should be redone; the formula for what is called the standard deviation is in fact the formula for error; and the Bessel adjustment, n/(n-1), is not necessary.

In a hyperbolic universe, when there is no error, every moment about the mean should be 0, not just odd movements where the moment is expressed as powers of i; and even powers which are multiples of i2 , are expressed as a real number, - 1.

The universe has a variance of .822,  and thus its standard deviation can never be 0.

So being unable to show my work, I can only assume that the above are true, but I can not prove that the above are true.