Growth

 

I’ve Got The Power

I've got the power (Power, power)
(You could break my heart, you could break my heart apart)
(You could break my heart, you could break my heart apart)
I've got the power (Power, power)
(Oh-oh-oh-oh)
I've got the power (Power, power)

You don’t WANT the power! You need an exponential.

Thinking about the future, forecasting/planning, has a long history in ….history. The simplest approach to forecasting, is to assume that it is like the past. This can take the form of trend analysis, but it is also why forecasting models are VALIDATED, based on historical data, to ensure that the present is consistent with the past, and those models are “backcast” to see how well a model “predicts” the past.

The simplest form of forecasting is to assume that there is a straight line from the past to the present to the future, where a simple Annual Growth Rate, AGR is used.

Future=Present+(AGR)*Years_{(from present to future)}

This does not acknowledge the fact that the years between the present and the future should also be considered, i.e. that compounding should occur. One of the songs in Mary Poppins, “Fidelity Fiduciary Bank” https://www.youtube.com/watch?v=XxyB29bDbBA goes into the glories of compounding. When loans or investments are made, it is typical to state a Compound Annual Growth Rate, often abbreviated as a CAGR. Compounding can be decibed mathematically as a power function.

Future=Present *(100%+CAGR)^years_{from present to future}

which can be restated as a power function of the form, y=a*b^x, where y is the future, a is the present, 100% + CAGR is the base, b, and the x is the number of periods, years, which have elapsed between the present and the future. This also means that it is possible to calculate a CAGR if you have a present value, a future value, and the number of years, periods, between these values.

CAGR=(Future/Present) ^(1⁄(years _{from present to future}⁾⁾ -100%

This assumes that the rate of growth is constant. An alternative function to growth is an exponential function which only requires that the growth be continuous, NOT continuous and constant. E.g. it is quite easy to grow in the early years, but very hard to grow in the future years.

Future=Present*exp (λ*years _{from present to future} )

The base in this case, exp(x), is the function of the special irrational number, e, the Euler number. This  can also be written as a power function, y=a*e^x, where y is the future, a is the present, e is the Euler number, and x is λ times the period, years, from the present to the future. In the special case when λ=1 and CAGR=e-100%, the power and exponential functions are identical.

This equation might be more familiar as a decay function when λ is less than 1, which if the future is considered to be event 1 and the present is event 2, is equivalent to saying the elapsed years between event 1 and event 2 are negative, i.e. the future occurs after the present. A half-life is given to the term  in a radioactive decay function and is proposed as the name given to λ, even when the elapsed time is positive, growing and not decaying. The “half-life” can be simply computed as

λ=ln (Future/Present)/years _{from present to future}

Exponential growth is an outcome of maximizing entropy. Maximizing entropy is implicit in many of the tools that Cambridge Systematics, the firm at which I work, uses: e. g.

·       Frataring;

·       Trip Distribution ( i.e. A.G. Wilson’s Gravity Model);

·       Mode Choice ( e.g. logit models);

·       ODME ( a digression ODME is the trade name given by Caliper. The generic name is Maximum Entropy Matrix Estimation);

·       Stochastic assignment (i.e. use of a logit equation to select among efficient paths);

·       bridge deck and pavement deterioration;

·       capacity investment decisions;

·       reliability.

Cambridge Systematics’ motto is “Think Forward” where those two words are separated by a stylized CS. (another digression. I have always translated this as “Thinking Ahead” inside of a diamond safety warning sign). If Cambridge Systematics is thinking ahead, I hope in the future we consistently always do it as an exponential rather than as a power function. Do not use a CAGR. Compute the half life. Growth is not constant, it must be resilient. That is why Ponzi schemes do not work.

Priceless

 

Ain't Got You

I got a house full of Rembrandt and priceless art    
And all the little girls they want to tear me apart   
When I walk down the street people stop and stare
Well you'd think I might be thrilled but baby I don't care   
'Cause I got more good luck honey than old King Farouk    
But the only thing I ain't got baby I ain't got you

What do you do when things are priceless?

“There are some things that money can’t buy, For everything else there is MasterCard.” So went an advertising campaign in the late 1990s. Economics is about allocating scarce resources.  The most familiar, but not the only way, of allocating resources is setting a price.  So what do you do about setting a price for something that is priceless?  There is also the problem that what is priceless to me, might not be priceless to you. To me, being able to attend the Red Sox 2004 Duck Boat Parade, priceless. To my brother, who is not a Red Sox fan, worthless. There is also the recent brouhaha about $5000 tickets to Bruce Springsteen concerts. ( and the lyrics listed above are from a Bruce Springsteen song). Fortunately, the Boss is not charging $5000 a ticket or the anger would be directed at him.  Instead the ire is directed at Ticketmaster. Their defense is that they are merely charging surge pricing, the same as airlines and hotels.

This assumes that pricing is the only way that a scare resource can be allocated.  It is not. My wife is a runner, I am a sitter, but an example from the running world is instructive.  Marathon bibs are a scarce resource. More people want those scarce bibs than there are bibs available.  The bibs could be auctioned, but that would incur ill will from those runners who can’t afford the price.  Most marathon organizers do not even want the money that could potentially be raised from an auction ( it is not that they want no money, it is just that they don’t want that much money).  Additionally if bibs were offered only to the highest bidders, eventually the losers would eventually not even bother to bid on the bibs and at some point in the future, there might not even be enough runners to keep the race going.  Also some of the runners are so desirable (elite) they should get bibs, even if they do not can’t afford/won’t pay that auction price.  But awarding the bibs on merit, say a qualifying time, is hard to manage and is also discouraging to those who can’t make the time but are willing to bid high on the price.  The bibs could be  awarded randomly ( and this is not a technological challenge.  When I went to a Rolling Stones concert in 1972 at the old Boston Garden, yes THAT concert, the tickets were allocated by a mail-in lottery. )

The most successful marathons allocate bibs on a combination of all of these approaches:

·       Auction ( where the bibs are actually awarded to charities who manage and get the proceeds from any auction);

·       Merit ( which does not have to be say qualifying times to get the elite runners.  It can also be volunteering at events, or as Pearl Jam offers tickets, membership in its fan club) ; and

·       Random  ( and by that, I mean truly random, and not the rope drop, or line sitter, or online multi-screen hacking and bot infected  “lotteries”)

Then you can allocate the scarce resources without having to set a price on something that to someone is priceless.

Intellectual Property II

 

Woodstock

By the time we got to Woodstock
We were half a million strong
And everywhere was a song
And a celebration

Should the music be free?

In 1969, I was at the Newport Jazz Festival that was cancelled mid-performance because the fences were stormed.  Consequently, I did not go to Woodstock because I made the false prediction that it would also be cancelled mid-performance.  To show how good my instincts are, I also attended the Newport Jazz festival in 1971, the one that was cancelled mid-performance while Dionne Warwick was singing “What the World Needs Now” and the fences were stormed.

The problem is not that music should be free, as at Woodstock, or cancelled, as at the Newport Jazz Festivals.  One of the first things that the US Congress passed in 1790 was the copyright protection act.  If you do not protect Intellectual Property, like music, and the performers and copyright holders are not paid for their Intellectual Property then they have no incentive to create or perform.  You might wish their work was free, but I bet they don’t.  If wishes were horses, beggars would ride.

Both the Newport Jazz  Festivals and Woodstock were problems in that the expected and protected attendance did not match the actual attendance.  Newport cancelled.  Woodstock 1 gave up.  Once festivals figured out how many people would attend and figured out a way to collect admission fees from the attendees, which the festival, the attendees, and the performers all thought was fair, and like Bonnaroo, Woodstock 2 and 3,  Burning Man , Coachella, etc., etc. festivals happened.  Music, like all Intellectual Property,  isn’t free, and if the system is fair, then everyone will agree that it should not be free.

 

Alito

 

Everybody’s Crying Mercy

A bad enough situation
Is sure enough getting worse
Everybody's crying justice
Just as soon as there's business first…

Straight ahead, gotta knock ‘em dead
So pack your kit, choose your own hypocrite

Render unto Caesar, the things that are Caesar’s, and to God, the things that are God’s

You would think that Justice “Strip Search Sammy” Alito would know the meaning of justice. But you would be wrong. In his “egregious” majority opinion. he confused his legal obligation to administer  justice with his moral view.  He was not asked to rule if abortion was moral.  He was asked to rule if it was legal.  This was no different than when the Pharisees, who opposed Roman rule, wanted Jesus to either oppose Roman rule and taxation, or accept Roman taxation and discredit himself.  They thought that they were giving him a classic “Have you stopped beating your wife?” question, where you are damned if you answer yes or no. Instead Jesus responded that the question was wrong and asked for a coin, on which was  Caesar’s face, and stated that “Render unto Caesar the things that are Caesar’s, and to God the things that are God’s”.  In the NBC sitcom The Good Place, Chidi is faced with the classic ethics Trolley Problem where he is asked to choose between saving 5 people or  saving 1 person.  He “solves” the problem by finding the choices wrong and opts instead to sacrifice himself.

It is especially ironic that "Justice" Alito chose to mock the free speech of others that did not agree with him, given the setting. That mockery might be forgivable if that person resides in France  or Canada, but among those he cited was the Duke of Sussex who resides in, and is supposedly covered by, the Freedom of Speech in the First Amendment to the US Constitution.  “Justice” Alito did not mention that his was not a unanimous decision and did not call out Justices Breyer, Kagan and Sotomayor or Chief Justice Roberts for dissenting from him.  The Duke of Sussex was mocked by “Justice” Alito for not only not agreeing with him, but comparing Alito’s  actions to Putin’s invasion of Ukraine.  Aside from the concept of free speech , which “Justice” Alito does not seem to get, he acted as if this was a domination game by his SCOTUS majority, which is not very different than the domination game played by Vladimir Putin.  That he was speaking at a forum on the freedom of religion is especially ironic.  Freedom to agree with his religion, I guess. Clearly, he don’t know the meaning of the word.

Transitions

 

Circle Game

And the seasons, they go round and round
And the painted ponies go up and down
We're captive on the carousel of time
We can't return, we can only look
Behind, from where we came
And go round and round and round, in the circle game.

After more years that I care to admit,  I have circled back to the beginning.

When I was a child at St Paul’s School, I was fascinated by the story of God’s casting of Lucifer out of heaven, so much so that I chose the name Michael, after the archangel Michael, as my confirmation name (which might not mean something unless you are Catholic, but this was a big deal to me!)  In high school I was enthralled by the Isaac Asimov’s idea of psychohistory as promoted by Hari Seldon in his Foundation novels.  ( And Apple TV+. A fancy Rubic’s cube for psychohistory?!  Is that the best that you could do?).  However I was born poor and decided that I would have to study it as an engineer.  In my hubris I applied to MIT. My application was rejected and I had to attend my safe school Brown.

(I am grateful to MIT.  I also applied for graduate school at MIT and while I was accepted at UPenn, I kept stalling them because I was waiting to hear from MIT, which eventually rejected me.  But while I was stalling,  UPenn kept increasing their financial offer, and MIT's delay paid off  in a dividend to me in the long run).  But back to Brown.  While at Brown, the closest thing that I could find to psychohistory was Jay Forrester’s (of MIT!) model and land use models. )

Land use modeling was not funded but transportation modeling, which used land use modeling,was, and that determined my course of study. I took a transportation modeling course in my senior year at Brown that was taught by Dr. Stella Dafermos, which I did not know at the time was the one of the developers of the User Equilibrium, UE, assignment  that would be a large part of my career.  My mother was a clerk in the department where her student Anna Nagurney showed that the best impedance function in UE, among the ones she tested, was a fourth power function, That was the basis for the use of  the Bureau of Public Roads, BPR, curve which had a fourth power component, as the standard impedance/Volume Delay Function, VDF.

The Atlanta Regional Commission adopted VDF curves that varied by Time of Day.  The reaction of my colleagues was that was nonsense because the VDF curve should be based on the physical behavior of vehicle and that should NOT vary by Time of Day, but instead should only be a form of thr BPR curve.  When I had the chance to investigate travel reliability measured as time, I found that reliability DID vary by Time of Day, because the drivers in different time periods had different expectations of reliability.  I speculated that the VDF curve was based on the combination of the behavior  of vehicles AND the driver’s of those vehicles.  In trying to include reliability in the VDF, I was forced to propose a new speed-volume curve, which had a transition from laminar, orderly, flow, to turbulent, chaotic, flow when the volume approached capacity, just like the behavior of fluids in pipes.  Since I have found an underwhelming response to this curve, I was forced to seek other metaphors.  One is that as you approach an absolute, i.e. capacity, you may transition from an orderly domain to a domain governed by chaos/entropy. 

Which leads me to propose that Lucifer was NOT cast out of heaven by God.  He cast himself out of heaven by trying to be too much like/approach God.  Which completes my circle.

Luck

 

I’d Rather Be Lucky Than Good

I’d rather be lucky than good,
Tough than pretty,
Rockin in the country than rolling in the city.
Spend my life rolling them dice,
Instead I’m living like everybody says I should.
I’d rather be lucky, rather be lucky than good.

Would you rather be lucky than good?

Einstein’s discomfort with Quantum Mechanics was that ”God does not play dice with the universe.”  His objection was the random element of luck in Quantum Mechanics. This random element is summed up in the Heisenberg  Uncertainty principle, which says that there is an intrinsic random error such that if you know the momentum exactly, then you can not know the position exactly,  and if you know the position exactly, then you can not know the momentum exactly. The minimum position is also known as the Planck length. A hyperbolic universe, spacetime, is consistent with this minimum, Planck, length.[1]

If you know the minimum time, and the minimum energy density,  then the Planck length is an outcome of the Einstein field equations for general relativity and a hyperbolic universe. Thus the quantum randomness is a consequence of the hyperbolic universe. It means that we can not construct equations in this universe that can eliminate this randomness. This means that God DOES play dice with the universe, but he uses a loaded dice in that he knows the outcome, but we can’t. If you want to be like God, then you don’t need to be lucky.

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

Forever

 

On A Clear Day

And on a clear day...
On a clear day...
You can see forever...
And ever...
And ever...
And ever more...

So far is forever?

Because the universe is locally flat, Euclidean, we might think it is universally flat. However it was proposed that universe is hyperbolic and it only appears flat locally. [1] I am copying a figure from that article because it shows curved spacetime, ....and because it is so darn pretty.

Treating spacetime as hyperbolic solves a number of problems,  not the least of which is estimating the size of the universe.

A hyperbolic universe has to be expanding after the Big Bang. Dr. Mabkhout’s article presents equations, based on Einstein’s equations and a hyperbolic curved spacetime, which is consistent with the age of the universe. A flat universe has to resort to dark energy and dark matter to explain the expansion of the universe and the inconsistency between the age and size of the universe. However if the universe is hyperbolic, without resorting to dark matter or energy, the implication is that the age of the universe, 14 billion years, is consistent with the size of the universe, 1.3 x10²⁸ cm, 8.6 x 10²² miles, 14 billion light-years. Of course since the universe its still expanding, check back in a few billion years and there will be a different answer for forever.

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