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.

Discount Rate

 

The Entertainer

I am the entertainer
The idol of my age
I make all kinds of money
When I go on the stage
Ah, you've seen me in the papers
I've been in the magazines
But if I go cold I won't get sold
I'll get put in the back in the discount rack
Like another can of beans

What should be the rate in that discount rack?

If the universe is hyperbolic, perhaps the discount rate, how much the future is worth compared to the present, is a fundamental constant of that universe.  The odds of a choice, which is defined as1where 0 is not making that choice, is 0.5.  That means that at its median, 50% will have made the choice and 50% will not have made the choice.  Let’s call 0.5 the range, s, of the choice.  Then the square root of the variance according to a normal logistics distribution of choice is 0.5*√3/π.  This number is 0.9067, or “A bird in the hand is worth 1.1027 (its inverse) in the bush.”  This means that the discount rate is 1/.9069 -100% or 10.27%.  If the interest rate is less than 10.27%, the universe is telling you that the cost of investing, on average, will have a positive rate of return. If interest rate is greater than 10.27% then the universe is telling you that the cost of investing, on average, will have a negative rate of return.

This might explain why humans as a group get nervous when the interest rate of a loan is much higher than 10%  It is only when the repayment is in future inflated dollars that higher interest rates may be tolerable. This discount rate also assumes that the asset being acquired is fully productive during its life and it is not depreciating. If it is depreciating, then that should be subtracted from the discount rate.  However, if an asset can be sold for 5% of its present value after 20 years and produces full value over  those 20 years, it is only depreciating by 0.25% per year.

Quantum Entanglement

 

Spooky

In the cool of the evening
When everything is getting kinda groovy
I call you up and ask you
Would you like to go with me and see a movie
At first you say no you've got some plans for tonight
And then you stop and say, "alright"
Love is kinda crazy with a spooky little girl like you

Maybe it isn’t so spooky after all?

Given the Heisenberg uncertainty principle, and the superposition of particles, isn’t quantum action at a distance inevitable, not spooky.

For example, take a deck of cards.  Divide them into one deck of red cards and one deck of black cards.  Turn the two decks over and shuffle them so that you can’t tell which deck is which.  Pick two cards from one deck but do not look at them.  You do not yet know the color of the card. Now look at the first card.  If it is red then that means that every card in its deck was red.  Now if you look at the second card, it is ….surprise, surprise…. red.  There was no need for communication between the first and second card. Any distance separating the cards is irrelevant. By observing the first card, which had not yet been observed, you could be certain of the color of the second card.  This isn’t spooky, it’s statistics.

Schrodinger’s cat, before it is observed, has odds of being 50% alive or 50% dead.  But the unobserved odds have nothing to do with the cat.  The cat will be either 100% alive or 100% dead but you will not know until you open the box, observe it.  The odds are NOT the result.  The odds of a coin flip are 50% heads.  But the result of every coin flip will be either 100% heads or 100% tails. There is nothing spooky about that.

Inflation VIII

 

Catch The Wind

For me to love you now
Would be the sweetest thing
That would make me sing
Ah, but I may as well, try and catch the wind

Raising the Prime Interest rate to control inflation may be trying to catch the wind

In being asked to control inflation by raising its interbank interest rates, the Federal Reserve Bank is using its primary function, to serve as the lender of last resort for private banks, in order to try to control random events. In doing so, it may doing more harm than good. The interest rate hikes may have contributed to private bank failures, and preventing bank failures is precisely why the Federal Reserve was created in the first place.

Banks exist to take existing liquid value and convert it to long term but less liquid future streams of value. When that value, a currency/medium of exchange, is based on a commodity there is a problem. Using a commodity as the medium of exchange in economic transactions means that you have to store, safely maintain, and transport that commodity. When that commodity is gold, this is not a trivial issue. Gold is heavy. Banks started issuing notes that represented a certain amount of that commodity. But that imposed a burden of trust on parties when using those bank notes. Both the buyers and sellers in economic transactions have to trust the bank and the value represented by its note.

When a currency, the medium of exchange, is a commodity that creates problems when groups hoard that commodity, corner the market. Then only economic transactions by those parties can be accommodated, which is precisely the opposite of the purpose of a medium of exchange. Trading by barter requires that both parties want what the other has and value their goods the same way. Since you can’t always find such parties, medium of exchanges were used to measure the value of goods. When the medium of exchange is a commodity, like gold, it is a commodity currency, and as mentioned when groups hoard that commodity and will not participate in exchanges, then the number of economic transactions declines. That is why fiat currencies were developed that are not finite and the market can not be cornered. The fiat currency should be sufficient to allow economic transactions to take place, including any increases in value, and you have to trust that the party issuing that fiat currency. If they set it to an amount that is more than the economic transactions it must support,  such as with the Weimar Republic, hyperinflation can result. That is why national economies usually set their currency to the value of their economy, e.g. M2. If that was the only economic transactions that needed to be considered, then that should suffice. The problem trade between nations with their own currencies.

During World War II, it was realized that gold as the international trading medium of exchange,  could not accommodate international trade because almost all of the world’s gold was in the Untied States and an international fiat currency did not exist. During Bretton Woods, John Maynard Keynes proposed the creation of Bancor as the international fiat trading currency. The problem was there was as yet no trusted group to issue such a fiat currency. John Foster Dulles and the United States prevailed in an argument that the US Dollar, while a fiat currency domestically, would be convertible into gold for international trade, a commodity currency.

This dual status of the US Dollar, a fiat currency domestically and a commodity currency internationally, was maintained until the Nixon Shock of 1971. At that time, the US Dollar was became a fiat currency at home AND in international trade. However the dollars in circulation were only created to support the value of the US domestic economy, M2. There was no recognition of the value in international trade that was supported by the US Dollar. As domestic  US Dollars competed with international US Dollars, the result was inevitable as the high inflation of the late 20^th Century. Arguably the fiat value of  the US Dollar should be M2 PLUS the USD used in international trading, MI. International trading has been increasing by 6-8 percent per year and the USD used in international trade, which according to the Society for Worldwide Interbank Financial Telecommunications, SWIFT, is approximately 50% of that trade. Thus the fiat value represented by the USD should be the current USD plus the change in M2 plus 50% of the change in all currency in MI. Measuring inflation over the last year includes changes in product inflation AND changes in currency inflation over the last year. While Year Over Year inflation has been declining and has been  as recently as 2020 been about 2%, long term inflation in  the CPI since 1971 has been about 4% per year. The pervasive inflation is because in those periods where random product inflation is zero or negative, there still has been an increase in currency inflation.

Arguably the Federal Reserve should only be concerned with currency inflation. However by setting the US Dollar only to accommodate the changes in M2, this ignores any changes in MI. It is proposed that the money supply of the US Dollar should recognize its use in MI. In this case, currency, medium of exchange, inflation should be zero. The problem is that inflation also includes product inflation. The Federal Reserve Bank tries to address product inflation by changing its Prime Inter-Bank Interest rate. In all honesty it can not do this. At best it can time-shift supply and demand, but it can not create or remove this supply or demand. The problem is that banks turn existing liquid value into illiquid future values. Withdrawals, if any, are from liquid reserves. If the withdrawals exceed the liquid reserves, then long term illiquid assets may be sold at a loss to turn them into liquid assets. If there are no buyers, or the loss is too great, then the bank fails.

A billionaire investor, e.g. Peter Thiel, withdraws his deposits/value from a bank, e.g. Silicon Valley Bank. While the bank has already converted his liquid value into streams of illiquid future values of a greater amount. However when each investor withdraws, that investor is allowed to withdraw liquid assets from the bank's reserves rather than receiving the converted illiquid value. The result may be a bank failure. The action precipitating the withdrawal may have been reduction of the future value of the stream of illiquid value because of the raising of interest rates. By continuing the fiction that the deposits have not already been converted and allowing them to be withdrawn from liquid reserves, the very act of raising the interest rates may have precipitated the bank failure that the Federal Reserve was created to prevent. You can change the impact of numerous random events. i.e. climate, setting the house odds. You can not control every random event, i.e. weather, each roll of the dice. Trying to do so is as futile as trying to catch the wind.

Normal

 

A Wonderful Guy

I'm as corny as Kansas in August,
I'm as normal as blueberry pie.
No more a smart little girl with no heart,
I have found me a wonderful guy!

You might be normal, but are you hyperbolically normal?

A hyperbolic normal distribution is proposed to be one in which 1/3  of the observations, outcomes, fall within the median ± σ and 100% of the outcomes fall within the median ± 3σ.  As in any normal distribution, the median will be equal to the mean, but the mean can be computed without ordering the observations.  

This also indicates that the minimum number of outcomes must be 3 or a hyperbolic distribution will be abnormal.  For example for two outcomes, e.g. a two player game, a choice/transition/phase change, will have a variance, σ² , but it will be hyperbolically abnormal because while it passes the 100% test, it fails the 1/3 test.  By contrast three‑or‑more‑players will always pass  both the 100% and the 1/3 test.  The variance, σ²,  of a two outcome game is 0.277777 which makes the range, σ, 0.166667.  If choice one has a value of 1 and choice two has a value of 2, then the median and the mean are both 1.5.  However while both outcomes pass the 100% test in that they are within 1.5  ± 3*(0.166667), they fail the 1/3 test in that neither outcome is within 1.5 ±  0.166667.  By contrast, a three player outcome: 1, 2, or 3; has a variance, σ², of 0.111111, or 1/9, which means that σ=1/3.  This distribution has a mean of 2 and a median of 2.  One hundred percent of the outcomes are within 2 ± 1, and 1/3 of the outcomes are within 2 ± (1/3).

The hyperbolic skew is proposed to be the ratio of the mean and the median.  When the ratio is greater than 1, the distribution  favors higher outcomes.  When the ratio is less than 1, it favors lower outcomes.  A hyperbolic normal distribution is one where this ratio is between 0.75 and 1.5 . In these cases, the observations will pass both the 100% and 1/3 test but the lowest observation will also not be less than 0.  When the median is equal to the mean of course the hyperbolic skew is 1.

It is not surprising that the minimum number of outcomes in a hyperbolic normal distribution is 3. In game theory there is a different strategy for playing two-player games and three‑or‑more‑player games.  If there are only two players in a game, then there have to be three outcomes: e.g. win, loss, and tie.  Having only two outcomes is abnormal.  If there are only two outcomes, you can not tell if the outcome is due to chance or the winner is better than the loser.

Bank Runs II

 

Honey in the Honeycomb

There's money in the savings bank
And I personally guarantee
If there's honey in the honeycomb
Then, Baby, there's love in me

So what is a bank?

A bank is a time machine.  It takes value that has been accumulated in the past and turns it into a stream of future values.  The problem is that it follows the laws of entropy such that the process is not reversible, while runs on banks pretend that it is reversible.  A run on the bank is an attempt to pull the accumulated value from the bank, without any acknowledgement that the value has already been converted.  You can’t do that.  As George Bailey famously explained in the run on the bank in the movie It’s a wonderful Life.

“you're thinking of this place all wrong As if I had the money back in a safe. The money's not there.  Your money's in Joe's house.

(to one of the men)

Right next to yours. And in the Kennedy house, and Mrs. Macklin's house, and a hundred others. Why, you're lending them the money to build, and then, they're going to pay it back to you as best they can. Now what are you going to do? Foreclose on them?” 

When you withdraw money from a bank, the bank it actually makes that withdrawal from its reserves to prevent the  need to foreclose.   Only when the withdrawals exceed its reserves, does the bank have to think about foreclosing. Just because you don’t see the sausage being made, does not mean that it is not sausage.

Hyperbolic Statistics

 

Natural Gift

You don't have to be a genius to find
All the hidden potential deep in your mind
You don't have to know about nuclear physics
Know all the formulas and vital statistics
You don't have to be an intellectual, you don't have to be a scientist
To use your natural gifts, you got natural gifts, yeh
Use your natural gifts, you got natural gifts

Coming soon to a math journal near you.  Hyperbolic statistics!

The first moment of observations about the origin is:

m₁=(1/n) ∑f_i x_i,  , summed from i=1 to k

where the index i is the i^th grouped observation, f_i is the frequency of that observation, (e.g. if there are 3 observations of 2, this makes 3 the frequency of the group of observations that is 2), k is the number of groups, and n is the number of observations. This is also the formula for the arithmetic, computed, mean, x̄ , often called the average. The average is more properly defined as the centrality of the normal. The median is the centrality, but in a normal distribution the mean is also equal to the median. Therefore saying the average is the mean is only true when the observations are also normally distributed.

The second moment about the about the computed mean, often called the variance, is:

m₂=(1/n) ∑f_i (x_i- x̄)² summed from i=1 to k

The square of the Standard Deviation is also often defined as the variance. In flat Euclidean space, the Standard Deviation, S.D., is: 

Euclidean S.D.=square root(∑f_i (x_i- x̄)²)/(n-1))

However this is only true in Euclidean space since it relies on Pythagoras’ Theorem for a hypotenuse. On a non-Euclidean surface, this is not the correct formula for the sum of squares. For example, the shortest distance between two points, a, and b, on the spherical surface of the Earth is the Great Circle Distance. According to Pythagoras’ theorem for a spherical surface, where R is the radius of the surface, e.g. the Earth, this is R*cos^-1(cos(a/R) *cos (b/R)). When the distance between points a and b is very small compared to the Radius, e.g. of the Earth, of the surface, then this is virtually indistinguishable from the traditional Pythagorean theorem.

If the surface is hyperbolic, not spherical or flat, then the shortest distance between two points is
cosh^-1(cosh(a)*cosh(b)). If a is defined as the summation of the deviations about the mean, and b is defined as 0, then the Hyperbolic Standard Deviation is

(cosh^-1 (cosh( (∑f_i (x_i-x̄))/n)))^(1/2)

while the Euclidean, flat, S.D is as defined before.

When the number of observations, n, is very large, and the sum in the second moment is not zero then there is virtually no difference between the hyperbolic S.D. and the flat, Euclidean traditional S.D. This does not mean that the difference is not real, just that in many applications there is no observable difference between the hyperbolic S.D. and the traditional S.D. Even when the sum of the square of the differences between the observations and the computed mean is virtually indistinguishable from zero, the difference between the traditional and hyperbolic Standard Deviation is virtually indistinguishable for large n , as shown in the figure below.

With a roll of a traditional six-sided die, there are six possible outcomes, 1 though 6, which if the die is not loaded should follow a normal distribution. The mean outcome is 3.5. The median outcome is 3.5.  The Euclidean Standard Deviation is 1.7.  This requires that according to the 68/95/99 rule for normal distributions that 99.7% of the outcomes should fall between the mean minus 3 SD and the mean plus 3 SD. According to the traditional SD, this requires that 99.7% of the die roll outcomes should fall between -0.6 nd 7.6.  While this is true, a more useful metric might say that 100% of the outcomes fall between 1 and 6. This requires the variance, σ², to be .694 and the square root of the variance, σ, to be .833. Then 100% of the observations fall between the mean ± 3σ. The Hyperbolic Standard Deviation of a six-sided die role is .34.  According to the Hyperbolic SD, this requires that 99.7% of the die roll outcomes should fall between 2.48 and 4.56, which is also the incorrect variance. 

The reason that the square of a Standard Deviation might not be σ², the true variance, is because of error. The true mean is not necessarily the computed mean because the computed mean can contain error.

x̄=μ+ ε¯

x̄           =           The computed mean, (1/n) ∑f_i x_i,  , summed from i=1 to k;

μ            =          The true mean;

ε¯          =           The mean error, (1/n) ∑ ε_i,  , summed from i=1 to k. 

The moments about the computed mean will only have non-zero values if the computed mean is NOT equal to the true mean.  This is because  (1/n) ∑f_i (x_i- x̄)^r summed from i=1 to k is equal to zero for every moment r when there is no error.  If there is no error, then the square root of the second moment about the mean should not be solved using Euclidean mathematics, etc. The computed Euclidean Standard Deviation added the Bessel adjustment, n-1, in order that the square of the Euclidean Standard Deviation be closer to the True Variance. The Bessel adjustment is only necessary if the Standard Deviation is computed using Euclidean geometry. It should be computed using non-Euclidean hyperbolic geometry. If the computed mean is the true mean, then the variance should be other than the square of the Standard Deviation.

It is suggested that the Standard Deviation for a normal distribution where the mean error is zero,  appears to be 0.  This is also not the variance squared, σ^2, but this is the limit of the Euclidean Standard Deviation when the number of observations approaches infinity.  This suggests that the 100% of the values of a traditional six-sided die, where this hyperbolic SD is 1.90,  occurs between -2.2 and 9.2.  Thus it is suggested that the square of the Standard Deviation is NOT the variance.  It is suggested instead that the high observation and the low observation be identified.  If the distribution is negatively skewed then the computed mean minus the lowest value minus .003 divided by 3 is the square root of the variance, σ.  If the distribution is positively skewed, then the highest value minus the computed mean minus  minus .003 divided by three is the squared root of the variance. If the skew can not be determined, then the maximum of these values should be taken as the square root of the variance, 

A no/yes, heads/tails, off/on transition which occurs at μ is a normal distribution. The transition is from whatever choice is assigned a value of zero to whatever choice is assigned a value of 1. Then the median choice is  0.5, the mean choice is 0.5,  the true variance σ² is 0.028, and the square root of that variance, σ, is 0.167.  According to the rule of normal distributions this requires that:

  0.3% of the transitions from 0 to 1 will be made by μ-3σ, or μ-0.500;

  5%  of the transitions from 0 to 1 will be made by μ-2σ, or μ-0.333;

32%  of the transitions from 0 to 1 will be made by μ-σ, or μ-0.167;

50%  of the transitions from 0 to 1 will be made by μ;

68%  of the transitions from 0 to 1will be made by μ+σ ,or μ+0.167;

95%  of the transitions from 0 to 1 will be made by μ+2σ, or μ+0.333;

99.7% of the transitions from 0 to 1will be made by μ+3σ, or μ+0.500. 

Mathematically there is no difference between a transition that happens at μ+3σ and one that happens at μ-3σ. Or Biblically, the Parable of the Workers in the Vineyard (Matthew 20: 1–16). It is wrong to say that there is no variance in choice, transitions, even when there is no error. Mathematically there is a definite non-zero variance with every choice.

Intolerance

 

Humpty Dumpty

And all the king’s horsemen and all the king’s men
Couldn’t put Humpty together again

Wait, that’s not right, is it?

My wife and her sister have a small business on Etsy. On the items that they sell is a cloth book of the children’s nursery rhyme Humpty Dumpty. My wife’s sister designs the fabric, and my wife sews the fabric. The line above is how it appears in their fabric book. A disgruntled customer was upset because in her opinion it should  have been “all the king’s horses”,  not “all the king’s horsemen.”  She was offered a refund including shipping both ways if she retuned the book. She refused. She wanted the fabric to be reprinted and the book to be  changed. This was not possible. She wanted the book to be no longer sold to others because it contained an “error” and left a bad review because of that. In other words, she wanted her opinion to be imposed on others.

This sounds like someone who is concerned with the letter of the law and not justice, the spirit of the law. I bet that customer also thinks she is being a good Christian which makes her better than other religions, and non-Americans who don’t speak English and are not as white as her. Who is going to tell her that that Jesus Christ was a Jew, didn’t speak English, didn’t live in the United States and was not as white as her?

She also should realize  that her preferred wording is not the only way that the nursery rhyme has even appeared. According to Wikipedia the first appearance of the Poem in 1797 was

Four-score Men and Four-score more,
Could not make Humpty Dumpty where he was before.

In 1810 it appeared as

Threescore men and threescore more,
Cannot place Humpty dumpty as he was before.

Elsewhere in that poem, “Humpty” was spelled “Humpti” and “sat” was spelled as “sate” but that is another issue.

The current version did not appear until 1882.

The poem was thought to be a riddle, where Humpty Dumpty is an egg, which is speculated as Dutch slang for Egg. Which reminds of an English coworker who triggered a spit take by me when he made the comment that he spent the weekend "knocking up" an old girlfriend. He meant that he “was visiting”,  not what I thought he meant. Two great civilizations separated by a common language indeed! The motto for the state of my birth is “Hope” which came from a misunderstanding by the early English settlers that the nearby Native American village was Mount Hope. The natives were saying “mantoup” in their language

From Wikipedia

In 1996, the website of the Colchester tourist board attributed the origin of the rhyme to a cannon recorded as used from the church of St Mary-at-the-Wall by the Royalist defenders in the siege of 1648.In 1648, Colchester was a walled town with a castle and several churches and was protected by the city wall. The story given was that a large cannon, which the website claimed was colloquially called Humpty Dumpty, was strategically placed on the wall. A shot from a Parliamentary cannon succeeded in damaging the wall beneath Humpty Dumpty, which caused the cannon to tumble to the ground. The Royalists (or Cavaliers, "all the King's men") attempted to raise Humpty Dumpty on to another part of the wall, but the cannon was so heavy that "All the King's horses and all the King's men couldn't put Humpty together again".

The poem has also been advanced as a story based on the Laws of Thermodynamics because once broken an egg, Humpty Dumpty, could not be but together again because its entropy has increased.

In any event, on this night when the 95^th Oscars are to be awarded, it is only a story anyway. If someone objects to how you are telling a story and calls you illiterate, they are probably projecting and confirming that they are illiterate, not you. Besides to be “woke” shouldn’t it be "horsepersons" any way. J

None of the Above

 

Complicated

Why'd you have to go and make things so complicated?
I see the way you're acting like you're somebody else
Gets me frustrated
Life's like this, you fall
And you crawl, and you break
And you take what you get, and you turn it into
Honesty and promise me I'm never gonna find you faking
No, no, no

A yes or no response isn’t enough

Facebook, I am told, allows you to set your relationship status as single, in a relationship, engaged, married, in a civil partnership, in a domestic partnership, in an open relationship, it's complicated, separated, divorced, and widowed. In this there are more than two options but even when there are only two responses, there should always be a third, It’s Complicated/Other. Thus a True/False quiz should be True/False/It’s Complicated. Otherwise you can be asked misleading “Have you stopped beating your wife?” questions, where you are damned if you answer yes (implying that you used to beat you wife but have stopped) or no ( admitting that you are currently beating your wife.). There always better be three options or the responses can’t tell anything.

This goes for any response/choice. If you are asked to choose between good and evil, you might choose to be 100% good or 100% evil, but you are not the only one making that choice. Each individual’s choice can be binary, but the sum of all choices is where we live.

AI

 

Dawn (Go Away)

Think (think)
What a big man he'll be
Think
Of the places you'll see
Now think what the future would be with a poor boy like me
Dawn go away

Thinking is intelligence, not inference

The topic du jour seems to be AI, Artificial Intelligence. This is, IMHO, an oxymoron. It really should be Artificial Inference. Computers (the Artificial part) are building inferences based on the data that they examine. However inferences are NOT always intelligent. Before Copernicus, the inference was that the sun moved around the earth. Before modern geology, the inference was that the Earth was only a few thousand years old. Before Michelson, the inference was that light moved though a luminiferous aether that permeated empty space. Before Einstein’s Theory of relativity, it was inferred that there was an absolute frame of reference.

The best that can be hoped from computers is that they will make inferences, discover a pattern in the data. It will be up to some one else to use intelligence to say what that pattern means.

Before you acknowledge that there is a pattern, make sure that you know what data has been examined. The Literary Digest famously predicted that Alf Landon would defeat Roosevelt in the Presidential election of 1936 because they had only polled their readers. If the data that AI is using is not inclusive, any patterns from that data will reflect its exclusions. You can’t make any inferences from data that you don’t have.

MAGA? II

 

Glory Days

Yeah, just sitting back, trying to recapture
A little of the glory, yeah
Well time slips away and leaves you with nothing, mister
But boring stories of

Glory days, yeah they'll pass you by
Glory days, in the wink of a young girl's eye
Glory days, glory days
Glory days, yeah they'll pass you by

Make America Great Again?

Make.  Good, an action verb.  Making things is progress. 

America.  The group to which you belong.  I’m with you. 

Great. What you aspire to. Now, that is inspirational. 

Again.  Uh.  You lost me there sport. 

Silly Rabbit. You can’t go home again.  You can’t recapture the glory days.  What has happened, has happened.  You can’t make the future look like the past. Anyone who tries to convince you otherwise is only tying to distract you.  MAG is fine. MAGA?  Not so much.

The Right Reasons

 

A Kiss From A Rose

Baby, I compare you to a kiss from a rose on the grey
Ooh, the more I get of you, stranger it feels, yeah
And now that your rose is in bloom
A light hits the gloom on the grey.

Before I give you my rose, are you here for the right reasons?

Some rules of thumb which I generally follow when I enter the voting booth, if I do not know the candidate. They are actually identical to the rules of thumb if I do know the candidate. A candidate for office is supposed to represent me to the group. I want someone who is for truth, justice, and the American Way. By that I mean that someone who acknowledges the truth; acts for justice for the group, not for himself; and promotes inclusion in the group (America is known for being a melting pot.).

A plus for being a woman and/or a member of a traditionally excluded group.

Women and others have too long been excluded from the group. Being a woman or a minority member does not mean that you aren’t in favor of exclusion (e.g. Ann Coulter, Kimberly Guilfoyle, Peter Thiel, Clarence Thomas, and Tim Scott) but hopefully you will be more sensitive to those who have traditionally been excluded.

A plus for being rich.

I do not think that the rich are smarter than others in the group. I just think that they have a higher price than anyone else, e.g. they have more to lose if they act for themselves and not for the group, and have a higher price such that only when the bribe is enormous will they act for themselves and not the group. The self-made rich are usually think first of themselves, but this may not be true of their descendants. That means I will give points to the descendants of the Kennedy, Roosevelts, and Rockefellers. E.g. Joseph Kennedy, Senior? No. John F. Kennedy? Yes.

A plus for being a veteran, a member of a non-profit, a teacher, etc.

I want someone who will act for the group, not for themselves. Veterans, Doctors Without Borders, Peace Corps volunteers, teachers, etc. have demonstrated that they place the interests of the group over themselves.

A minus for being a celebrity

I expect the Peter Principle to apply, that being good in one job does not mean that you will be good in another job. Being a great football coach does not mean that you will be a great senator. (E.g. Tommy Tuberville)

A minus for being in any form of show business.

I have to trust the positions that are, and will be, supported by the candidate. The art of show business is learning the art of distraction, the razzle dazzle, which means I can’t trust the stated position. That means I won’t vote for a Jane Fonda or an Al Franken, but I also won’t vote for a Ronald Reagan, Doctor Oz, or Donald Trump.

A minus for attending a top school.

This sounds counter intuitive. I attended a top school. Shouldn’t I want someone like me to represent me? Don’t I trust myself? (Uh…not really!). Attending a top school might mean that the person wanted to get the best instruction, but it also could mean that the person is merely doing resumé padding. I attended classes at the Wharton School while at UPenn, but Donald Trump, Donald Trump Junior, Ivanka Trump, and Elon Musk also all also graduated from Wharton.

A minus for being divorced.

Yes, I realize that there are people in unsuccessful marriages and those people are perfectly justified in getting a divorce. However when they married, they took an oath that they would be in that marriage forever. A successful candidate will also be asked to take an oath to support the group. That is an oath that I don’t want them to break.

The candidate who has a higher point total than their opponents, is the one who will probably get my vote. To use a line from one of my wife’s favorite shows, I want to give my rose to a person who is there for the right reasons.

Unconscious Bias

 I Don't Know Why (I Just Do)

I don't know why I love you like I do
I don't why, but I do
I don't know why you thrill me like you do
I don't know why, but you do.

Shouldn’t you want to know why?

Unconscious biases can be long lasting and may be …doh…. unconscious, something of which you aren’t even aware. Case in point. I attended Brown University where the Computer Science Building was funded by one of its alumni, Thomas Watson, Jr, a former CEO and son of the founder of IBM.

In the 1980s, IBM was introducing Personal Computers, PCs. They used a subcontractor to work on its operating system and that subcontractor had a competing version of the BASIC computer language, which ran on those PCs. That version of BASIC was obviously not to be taken as seriously as IBM's since that competing version of BASIC went by the name GW (Golly Whiz) BASIC. So clearly there was no serious reason to invest in that subcontractor when they had their Initial Public Offering. That subcontractor was, at time, a little firm called Microsoft. Being biased in favor of IBM did not work out so well for me.

When search engines were being developed, Scientific American did a review of two competing, innovative search engines. One was IBM's CLEVER. The name of the other search engine is the punch line. Needless to say, I was much more impressed with IBM’s search engine and saw no reason to invest in its no-name, fly-by-night competitor. The name of that competing Search Engine... GOOGLE. Another case of where being biased in favor of IBM led me to back the wrong horse.

As to how long-lasting unconscious bias can be, my father’s parents saw two of their children die in the Spanish Flu Pandemic, before my father was even born. My father had an abiding fear of public spaces, anything shared, that I am fairly sure that he learned from his parents, but he never acknowledged why. When I reflect on my response to the COVID pandemic, which was influenced by my own upbringing by my father, I had to reflect on this incident that happened before my father was even born.

A coincidence. The firm at which I worked since 1998, had its HQ less than a mile from where my Uncle and Aunt died and were buried. I do not know, but suspect, that their deaths were why my grandparents moved from Cambridge, MA to Providence, RI where both my father and I were born.