Hyperbolic

 

Yellow Submarine

As we live a life of ease
Every one of us has all we need
Sky of blue and sea of green
We all live in a yellow submarine

NO! We all live in an asymmetrical hyperboloid!

It appears as if the universe in which we reside is the turbulent lobe of an asymmetrical hyperboloid which is formed by rotating an asymmetrical  hyperbola about the about axis on which a transition occurs. This can be described  as a two-sheet hyperboloid, where there is no separation between the upper and lower sheets. That single point, the separation between order and chaos, might explain the Big Bang.

If the universe is hyperbolic, as proposed by Mabkhout, https://medcraveonline.com/PAIJ/non-dark-hyperbolic-universe.html, then there is no need to resort to Dark Matter or Dark Energy to explain the expansion of the universe. Expansion, and even inflation in its earliest stages, is instead a consequence of that hyperbolic surface. If the universe is hyperbolic, then there is no contradiction between the apparent age of the universe and the size of the observable universe. If the universe is hyperbolic, then there is consistency between the Planck length and the Planck energy. If the universe is hyperbolic, then the rotational energy of galaxies is a consequence of that shape and is not a paradox.

If the universe is hyperbolic, then Euclidean geometry does not apply for very large distances and very large speeds. (i.e. the universe is locally flat but universally hyperbolic). In a flat universe, the Euclidean equation for a hypotenuse becomes imaginary when the sum of the sides of a triangle is negative. If the universe is hyperbolic, then  the correct solution  for c²=a²+b² is NOT c=√(a²+b² ), it is cosh(c)=cosh(a)cosh(b). Einstein’s formula of Energy, E=mc² , implies a solution for the mass that is not m_0*(1/√(1-(v/c)²)), but should be ln(cosh(v/c)cosh(m₀)±sinh(v/c)sinh(m₀)). The first solution requires that the mass becomes imaginary when v>c. According to Einstein v can never exceed c. The Euclidean, flat, equation is imaginary when v>c and has a contradiction at v=c. (At the speed of light, it has to paradoxically be equal to both zero and infinity). The hyperbolic equation never becomes imaginary and has no paradox at v=c. Instead the equation only allows real solutions and is undefined if v exceeds c.

If the universe is hyperbolic, then gravity may be an apparent force, which is actually masses approaching a common center to minimize their respective energy and increase their entropy. If gravity is NOT a fundamental force, then there is no graviton to be observed, and there is no need to fit gravity into the Standard Model of Physics.

A normal equation of choice, where before the choice the value is 0 and after the choice the value is 1 (i.e. heads/tails, no/yes, off/on, false/true) has a odds of 0.5, but the outcome can only be 1 or 0.  The range, the difference between the choices, ( i.e., the median value of the Probability Density Function at the choice) is then, by definition, 0.5.  A normal distribution of discrete choice ( the logistics distribution) with a choice at µ, and range, s, of  0.5 is ½*sech²(x‑µ). The variance of this distribution is not 0 but it is 0.5*π/√3. If there is choice, then there must always be a variance and has to be greater than zero. A hyperbolic universe thus answers the debate about  a deterministic universe where variance must always be 0 and a random universe where the variance can be greater than  zero.

Variance is a consequence of reality approaching an absolute. Determinism requires a parabolic solution where reality can be equal to the absolute. Choice requires a hyperbolic solution where the reality can approach, but never equal, the absolute.

A transition occurs whenever a reality approaches an absolute. ( e.g. Speed on a road is separated into congested and congested domains at the capacity of the road; Flow in a pipe or channel is separated into laminar and turbulent domains as the flow in the pipe approaches the capacity of the pipe; The mass of a particle is hypothetically separated into subluminal and superluminal domains by the speed of light.)

This occurs because a transition ( i.e. change in behavior) has to occur whenever reality approaches an absolute. This transition arguably explains the shape of a curve in traffic flow, in Fluid Dynamics, or in general relativity. It also has a bearing on the correct computation of statistics. the formula for Standard Deviation is NOT a measure of the variance. It is a measurement of the error from the mean. Even if that is error is reduced to zero, the variance will still exist. This is why there appears to be positive moments around the mean when the moment is even, when Euclidean geometry is used. It is because the moment should actually be computed using hyperbolic, not Euclidean, geometry. Consequently, the even moment is because the Euclidian solution requires that the moments exist in an imaginary plane and every even moment in the imaginary plane becomes real, iⁿ=(√-1)ⁿ =-1 which is real not imaginary, when n is even. If statistics is computed using hyperbolic geometry, then every moment about the mean is zero when there is no error.

If the universe is hyperbolic and random, and random events follow a hyperbolic secant squared distribution and do not repeat, except in the imaginary plane, these random observations can be highly correlated with Euclidean geometry which repeats.  But correlation is not causation. Get real. We all live in a hyperbolic universe which is never imaginary.

Mediocrity

 

I Get Knocked Down

He sings the songs that remind him of the good times
He sings the songs that remind him of the better times
(Oh Danny Boy, Danny Boy, Danny Boy)
I get knocked down, but I get up again
You are never gonna keep me down
I get knocked down, but I get up again
You are never gonna keep me down

This Danny Boy never got up in the first place.  Getting up is WHY you get knocked down.

There is a strategy that I just discovered that sounds like my guiding principle, Strategic Mediocrity.  It is an investment strategy that says to achieve growth, the goal should not to be the best, because, things being random, the best may, on the next roll of the dice, be the worst.  “The last shall be first and the first shall be last", to borrow a phrase.  The best strategy is to be in the middle, to be mediocre, to not stand out.  If your goal is growth, then aim for the middle.

If your aim is anything, don’t be number one.  If you are number one, then there is pressure to remain number one.  If you are number two, then there is pressure to become number one and not slip to number three.  If you are number three, there is the pressure to become number one or two and not slip off the podium.  If you are just off the podium, then there is less pressure.

A whack-a-mole gets bopped on the head when it sticks its head out of a hole by itself.  If every mole stuck its head out of the hole at the same time, then the odds are reduced that any one mole will be knocked down. Encouraging others to stick their head out, at the same time as you, sounds like the safest strategy.   You are more likely to achieve your goal, be it investment, growth, wisdom, etc. if everyone does it at the same time.

John Maynard Keynes

 

Sloop John B

So hoist up the John B's sail
See how the mainsail sets
Call for the captain ashore, let me go home
Let me go home, I wanna go home
Let me go home

Oops, wrong ship. I thought this was the Sloop John M.

John Maynard Keynes proposed an international monetary system which would use the Bancor. The continued reliance on gold as an international medium of exchange would not allow for international trade because most of the world’s gold at the close of WWII was in the United States. The United States prevailed with a position that the US Dollar, which was a domestic fiat currency since it could no longer be converted into gold, should be convertible into gold internationally. This position was ratified at the Bretton Woods Conference of 1944 and endured until the Nixon Shock of 1971. As long as other nations who acquired US Dollars through international trading did not try to convert those US Dollars into gold, the system was a de facto international fiat currency. But because of the fear that other countries could convert those international dollars into gold, Nixon made the international convertibility null and void. Because the US money supply was only intended to accommodate US domestic economic transactions, e.g. M2, but not the international economic transactions, the result was the high inflation of the 1970s and 1980s and today's continuing persistent inflation.

A man can not serve two masters. It is also true that a currency can not be both a domestic currency and an international currency. The US has suffered continued inflation because of this situation. Another major international trading currency is the Euro, which is also the domestic currency within each country of the European Union. The Euro replaced the Drachma in Greece and the Lira in Italy, among many others. However when the domestic economic crises  in Greece and Italy required a deflation of their own domestic currency in order to address their  economic crises, they no longer had a domestic currency, It looks like John Maynard Keyes was right all along, ... again. The world needed an international fiat medium of exchange such as the Bancor. Not having one has resulted in many domestic economic crises that could otherwise have been avoided.

Regulations

Falling in Love with Love

Falling in love with love is falling for make-believe
Falling in love with love is playing the fool
Caring too much is such a juvenile fancy
Learning to trust is just for children in school

But regulation is for everyone, not just children.

There are regulations because, whether we like it or not, we can not trust everyone.  It would be wonderful if we could, but as a former president said ”Trust, but Verify”.  Ironically that same president also opposed regulation, meaning he and his group could not trust you, but you should trust him and his group.  Actually it doesn’t work that way.   An economic transaction requires a buyer, a seller, and goods to be exchanged.  Regulation is necessary for economic transactions to occur. As a convenience, so that economic transactions do not exist only in a barter system, there is typically a medium of exchange, a currency, that is traded for the goods and services being offered by the seller.

The economic transaction requires trust.  First the buyer has to trust that the goods and services offered by the seller are as they are presented. Because the buyer does not have perfect knowledge, he counts on the knowledge of others, the group, to vouch that the goods and services are as portrayed and can be trusted.  Similarly the seller has to trust that the medium of exchange is not counterfeit.  The medium of exchange in ancient times, was precious metal, especially gold and silver.  However having a scale and having  the skill to recognize that this was indeed a precious metal was not practical.  One of the earliest functions of civilizations was to MINT, that is weigh and assay precious metals, into coins, the medium of exchange.  If the exchange of some goods and service had to be regulated, then it stands to reason that there must be some goods and services that do not need to be regulated.

Unfortunately while economists study those transactions, they did not classify goods as regulated and unregulated.  The earliest classification of goods was into  a single dimension:  price.  But there is still a lot of variation even in this one dimension.  Priced goods can be expensive, inexpensive or free.  And the medium of exchange can be positive, i.e. wealth, or negative, i.e. debt.  Loans and debts are merely a way of time shifting the medium of exchange into the future.  But even within the single dimension of price, there are still shades of grey. 

Seeing things in shades of black and white is a step forward, but it is not perfect.  However rather than adding  a dimension for regulation, economists chose to subdivide price.  Goods and services are defined by economists as rival and exclusive.  Rival Goods are those that can not be used by another if you are using them.  (e.g. you and I can not both drive the same car at the same time). Rival goods are often further subdivided into durable, and non-durable depending on whether the good is intended to be consumed or continue after its use.  ( You eat an apple so it is non-durable.  A new car merely becomes used, can be driven sequentially, and thus is durable)  On the other hand there are goods that can be used by many people at exactly the same time. ( e.g. my listening to a concert does not mean that you cannot listen to that same concert at the same time).  Using this classification system, there are Private goods ( Rival and Exclusive, such as an apple) and Public Goods ( Non-rival and Non‑exclusive, such as sunshine).  In one dimensional thinking, private is thought of as priced and public is thought of as free.  However the two-dimensional system also allows for two additional classifications: Common Goods ( Non rival and Exclusive,  e.g. clean water) and Club Goods ( Rival and Non exclusive, e.g. concerts).  Buyers and sellers both agree that regulation should at least protect their interests in Private Goods and both agree that there is no regulation of Public Goods, but the buyers and sellers disagree as to how Club Goods and Common Goods should be regulated.

Buyers view Club Goods as unpriced. You should charge no price for my listening to a concert, because even if I do not buy it but merely consume it for free, that does not stop you from selling it to others.  However unless someone pays, there is no way to pay the artist who is creating that concert.  That is why one of the first laws passed by the US Congress was the copyright act to ensure that artists will produce goods.  At the same time the buyer was also protected by trademarking the goods so that the buyer could trust  the goods being sold.  But from the concert promoter’s, the seller's, perspective they are selling you admission and possibly a seat at the concert, not the music.  From the seller’s perspective, the good is the admission or the seat.  From the buyer's perspective, the good being purchased is the music, which is non-exclusive, and which might be mistaken as free.  The same problem exists for common goods.  They are not free. They are unpriced. This merely means that the transaction cost to collect a price may be greater than the value collected by that price, but that is not the same as having no value.

Regulations are an admission that the buyer may not trust the seller AND the seller may not trust the buyer, but each should be trusted by the group. In this case  the transaction can  take place.  No regulation, no trust.  Accepting regulation is not an acknowledgement that the you should not be trusted. Regulation is a means to ensure that the transaction can take place.

Mike Nichols ( the director of The Graduate) and Elaine May ( the director of The Heartbreak Kid)  used to be a comedy duo.  As such, they appeared in a series of TV commercials for Narragansett  Beer that ran during TV Red Sox games when I was a child.  YouTube does have an adaption of one that was used for JAX Beer.  https://www.youtube.com/watch?v=VkcdU4gxU38. "I'm not making fun of you. I'm making fun of her".  Regulation is not because I don’t trust you. It is because I don’t trust the other person!

E-Commerce

 

Mr. Postman

Please Mister Postman look and see 
Is there a letter oh yeah in your bag for me? 
You know it’s been so long 
Yes since I heard from this boyfriend of mine 

Is e-commerce freight, or just another postal delivery?

There has been considerable interest in the rise of e-commerce. It has prompted a discussion on whether e-commerce should be considered to be freight. It should be understood that what is called freight is only part of the transport of goods from a producer to a consumer.

Under a barter system, a producer trades goods directly with a consumer. If the producer and consumer are in the same place, there is no need to transport the goods. However in the event that the producer and the consumer are not in the same place, it might be the responsibility of the producer to carry the goods to a market where they are traded to the consumer. The movement of those goods to the market by a producer is not considered to be freight. The movement of those goods from the market under the control of the consumer is also not considered to be freight.

But if a third party, a carrier, was hired to transport the good by the producer or the consumer, it might be considered to be freight. In many cases the consumer makes a Home-Based Shopping, HBS, trip from their home to a market where goods may, or may not be, acquired. This HBS trip by the consumer is not considered to be freight, whether, or not, goods are transported. Additionally it is unlikely that goods are traded directly between a producer and a consumer. The producer will himself be a consumer, of raw material, and will only be a producer of finished goods. There may be several intermediate traders ( who are buyers from the producer and sellers to the consumer) involved before it reaches the ultimate consumer. It is this division of the supply chain into goods movement by the producer and transport within a Home-Based Shopping trip by the consumer that has led to the confusion concerning e-commerce. The movements are still the same but the handoffs and definitions of various pieces of the supply chain have changed.

If a consumer electronically contacts a producer and that producer uses a public service, e.g., the US Post Office, to transport the goods directly to the consumer’s home, there is no physical market. The market effectively becomes the consumer’s residence.

The transport of goods becomes freight when a carrier is paid to transport those goods. The movement of goods within the property of the producer is never considered to be freight but is instead considered to merely be a business transaction that is needed to produce the good. No one would consider the  transport of goods within a factory to be freight. Similarly if the producer moves a good from his own warehouse to his own factory, even if these locations are physically separated, this is typically considered to be a business transaction, not a freight movement.

If the producer or consumer has acquired a fleet of freight vehicles for other purposes, it may choose to transport the goods themselves rather than hire a carrier. The goods transported in these private vehicles, mostly trucks, are considered to be freight because if those vehicles were not available a carrier would have been used.

The reporting of information about freight will also be different depending on whether the information is obtained from the shipper/receiver, or the carrier(s). A producer may know the contents of a sealed container or a small package and may view the container or package as not relevant in their choice of carrier. However from the carrier’s perspective, they may not know or care about the contents of a container or package, and classify the goods by the package itself, e.g. Freight All Kind, rather than the contents.  Similarly a carrier may only know part of the supply chain, e.g. where his service is needed,  a warehouse, intermodal rail terminal, seaport, or airport, where goods are loaded and/or unloaded, not where they are produced and/or consumed. A shipper and/or receiver may be ignorant of these intermediate carrier stops. A shipper and/or receiver may distinguish individual shipments, but the carrier may consolidate shipments and the operation of their vehicles, not the operation of the shipments, might be optimized

Shown in the figure below is an example of a current supply chain with classifications as freight. That same figure shows the same movement reclassified as e-commerce. However in both instances the amount of goods movement is exactly the same. Whether the vehicles transporting those goods use more resources depend on whether the delivery is using existing resources ( e.g. US Postal delivery) or are using new trucks and the operation of those trucks requires more resources than the HBS trips they are replacing. E-commerce may be growing, but it may be merely reclassifying goods movement from non-freight or personal trips to freight. In other words, just because e-commerce is growing that doesn’t mean that freight is growing.

The reporting of freight and e-commerce data is highly dependent on the source of the data and the operations involved.  In the figure above, if the information is from the perspective of the shipper ( e.g. The Commodity Flow Survey, the Freight Analysis Framework, etc.), the carrier transfer point may not be identified; but if a carrier centric source had been used (e.g. Transearch, Carload Waybill, etc.) that carrier transfer location may be identified.  The first freight trip between the Producer and the Trader and the second freight trip between the Trader and the Retail Warehouse may not be linked.  If in-store pickup is used with e-commerce, no change from the current condition with an HBS trip may be expected. Otherwise e-commerce may replace the HBS trip.  If the e-commerce is directly with the producer, this e-commerce might be identified as an on-line direct-to-consumer purchase. If                    e-commerce is used it may only be a change in the warehouse, or might be directly from a trader. 

Reality

 

Imagination

There is no life I know
To compare with pure imagination
Living there, you'll be free
If you truly wish to be

Imagination is great, but sometimes you want reality!

Return with me now to my Sophomore Engineering class when I was taught  Electrical Engineering. In the unit on Alternating Current, where Alternating Current is a regular repeating trigonometric function of current ( a sine or a cosine), the output had a real AND an imaginary component. The engineers-to-be were being taught to discard the imaginary part. I never could wrap my head around that, ran away metaphorically screaming, and became a Transportation Engineer and NOT an Electrical Engineer.

The problem might have been that been that the output solutions should have been hyperbolic trigonometric solutions all along, which repeat only in imaginary planes. It the inputs are real then the outputs remain only in the real plane. (I.e. Real inputs have only real outputs). The imaginary solutions cancel each other and there are only real solutions anyway.

I.e. Given cosh(x) = cos(x)+j*sin (x) where j is the imaginary number, √-1,then any solution which is expressed as a combination of  imaginary numbers and real numbers can be expressed as a only a function of real numbers. So more than fifty years later I realize that I should not have run away screaming, I should have realized that what was being taught to me as imaginary was not only real, it was hyperbolic!

Global Trade

 

Nothing Lasts Forever

Nothing lasts forever, you should know that by now
Good times, heartache
You'll get through this trouble though you may not know how
Your heart won't break

International Trade may be growing now, but that growth won't last forever

Growth follows a sigmoid, S, curve, whether it is the growth of animals from birth to full adult size, the total population of an island, etc.  A simple sigmoid curve is the hyperbolic tangent function, tanh. If you know the period over which the trade is going from no trade to full trade, and you know the value of full trade, then it is possible to make predictions about the value of international trade.  Based on fitting simple linear approximation to the observations, it looks as if the growth of trade is happening over 100 years, from 1974 to 2074, and that the first 25 years will show modest growth, the next 50 years will show the highest growth, and the last 25 years will be a return to the previous modest growth before full trade is achieved.  It is going from virtually no trade in 1974 to $45 trillion in 2074.  The annual trade may be more or less than the amount forecast, but it would be even more wrong to think that the current growth rate will continue indefinitely.