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 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 crates 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 + 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 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.