"The Approximate Present Does Not Approximately Determine The Future"

Tyler Durden's picture

Chaos Theory turns 50 years old this year, celebrating half a century of flapping butterfly wings in Brazil creating tornadoes in Texas.  That most famous example is especially appropriate, since it was a meteorologist named Edward Lorenz who first outlined why seemingly consistent and knowable systems can still go wildly wrong.  As it turns out, as ConvergEx's Nick Colas reminds us, small errors in measurement or observation at the start of a time series can significantly change how things look at the end.  In the current low volatility, one-variable central bank driven global equity markets, Chaos Theory may seem a quaint relic of past crises.  However, its central lesson – that complex interrelated systems create unexpected outcomes from seemingly benign inputs – is still relevant.  Students of economics like to think of their discipline as scientific, just like physics or other hard sciences.  They would do well to embrace the intellectual honesty neatly encapsulated by the central lessons of Chaos Theory.


Via ConvergEx's Nick Colas:

If I asked you to name a famous weatherman, I doubt you’d come up with Dr. Edward Lorenz of the Massachusetts Institute of Technology.  No, he’s no Al Roker or Jim Cantore in terms of fame or fortune.  He never stood in the middle of a hurricane to report for the Weather Channel or walked through a devastated trailer park after a tornado.

Dr. Lorenz’s contributions, however, have a far wider reach because he is the researcher who came up with what we know today as ‘Chaos Theory’.  Here’s brief history of the man and his discovery:

  • Edward Lorenz was born in West Hartford Connecticut in 1917, attending Dartmouth (BA 1935) and Harvard (Master’s 1940).  He served as a meteorologist for the U.S. Army Air Corp. during World War II and earned two degrees from the Massachusetts Institute of Technology during and after the war.
  • At the time, weather forecasting was considered pretty simple stuff.  Take enough inputs from today’s climate and you should be able to forecast tomorrow’s weather pretty closely.  Simple, but not especially effective.  And potentially deadly for an air force during times of war, even the “Cold” one which followed the armistices of 1945.
  • Lorenz thought that the linear approach was wrong, and started working on non-linear algorithms to forecast the weather from his new seat as a MIT professor.  In the mid 1950s, he started to use an early computer – the Royal McBee LGP-30 – to help with the calculations.  Its clock speed was 120 kHz, about 100,000 slower than an iPhone 5.  It weighed 740 pounds.  But it was better than doing thousands of calculations by hand.
  • To speed up the calculations of the many iterations required for his research, Lorenz truncated the number of decimal places for the inputs to his model.  He then went back and added more detail to those same inputs – 2.212 became 2.212175 – to see if he got a more fine-tuned response.  To his surprise, those little tweaks created very different outcomes in his models.  Small changes to the “Base state” – today’s weather conditions, for example – could result in radically different expectations for the weather in just a few days time.
  • Lorenz published a paper on this phenomenon in 1963 – 50 years ago – titled “Deterministic Nonperiodic Flow.”  Yeah, not a very catchy name…  And according to a summary about the 50th anniversary of the paper in Physics Today, it garnered fewer than 20 citations in the dozen years after its publication. 
  • Lorenz’s observations begin to catch real traction only in the mid-1970s, when a paper titled “Period Three Implies Chaos” (Li and Yorke, 1975) gave his ideas a catchy name and a new audience: mathematicians and physicists.

In 1972, Lorenz gave a talk which he titled “Predictability: Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?”  This famous observation is almost as well-known as the term “Chaos Theory” itself, and serves to explain the basics of Lorenz’s discovery.  Three quick points here:

  • Lorenz’s 1962 paper summarized his findings this way: “For those systems with bounded solutions, it is found that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly different initial states can evolve into considerably different states.”
  • He later summarize “Chaos” more concisely as “When the present determines the future, but the approximate present does not approximately determine the future. 
  • In totally laymen’s language, Chaos Theory says that if you want to forecast the future you need to know everything about the present.  And by “Everything” we mean all knowable characteristics of today, in infinite detail.  Even if you have a great set of formulas in a comprehensive model about how those many variables interrelate, your predictions will run afoul of ‘Chaos’ – the ability of an overlooked (and typically small) characteristic of the starting point to have a large effect on the outcome.


In the world of economics and capital markets, Chaos Theory clearly resonates.  The Financial Crisis of 2007-2008 and its follow-on travails all have the gentle flutter of the butterfly’s wings somewhere at their core.  Small issues – a marginal residential development in Scottsdale, a deal by Greek monks for some Athenian commercial real estate – quickly cascade to become the tornado in Texas.   Or New York, or London, for that matter.

What I find most striking is the current market psychology that seems to think all the butterflies are dead, or at least safely in their pupae.  Observed volatility for stock prices, as measured by the S&P 500 Index, are trending lower over the last 10 and 20 days, even as the market itself reaches new highs.  Implied volatility in options contracts are trending lower as well.

It not just the math of volatility that I find most puzzling, but the notion that central bank policy is all that matters to economic and market outcomes.  I get the fact that the last few years have been humbling for everyone from risk-averse investors (who missed the move in risk assets) to policymakers who shovel liquidity into an economic system which still struggles to create jobs or growth.  But it seems very much like commentators and market participants desperately want to believe the world behaves according to simply rules.  “Just buy the equity market whose central bank has the largest bond buying program” is essentially the only piece of investment wisdom needed for the last 48 months.  And counting…

I keep coming back to Lorenz’s statement that "The approximate present does not approximately determine the future."  We know our approximate present very well, at least in the U.S.:

  • A slow growth economy
  • An accommodative central bank
  • Only one other large economy (Japan) with the appetite to follow our lead in buying large quantities of long dated bonds
  • A seemingly “Self sustaining” rally in stocks, where there is enough momentum to pull at least a few new buyers into the mix.  And low enough interest rates to provide few alternatives to investors.

At the same time, Chaos Theory is clear: this does not approximately determine the future.  There are more than enough variables out there – the butterflies flapping away – which can change outcomes.   Don’t get me wrong – this is not meant to be a doom and gloom closing thought.   If stock markets exhibited ‘normal’ volatility, it would be far easier to defend current price levels.  You could leave the butterfly net at home.  The problem is that current market price action –that slow steady grind higher – indicates marginal buyers don’t fret very much about the future.  No matter how little we really know about it.


Additional Reading

Original 1963 paper: http://eaps4.mit.edu/research/Lorenz/Deterministic_63.pdf

50th Anniversary in Physics Today: http://www.physicstoday.org/resource/1/phtoad/v66/i5/p27_s1?bypassSSO=1

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Headbanger's picture

War is Peace

Freedom is Slavery

Ignorance is Strength

Chaos is Order

InTheLandOfTheBlind's picture

first it is all relative, then it is absolute

Pure Evil's picture

When Chaos Theory bumbed into Chaos Reality, Obummer was pushed out of the vortex nine months later.

Diogenes's picture

If a pyramid is sitting on a bedrock base it can stand for 5000 years. If it is balanced on its point a butterfly can push it over. Chaos theory applies to unstable systems. Economic systems become unstable when given over to short term thinking, scams, and Ponzi schemes. When based on honesty and  genuine production of useful goods and services they are more stable.

Parrotile's picture

Maybe "Brace for Impact" might be more appropriate!!

Boris Alatovkrap's picture

Boris is choose "turbulence" because is enigma to engineer and physicist. "Impact" is fun, but done and over, kaput. 

TheEdelman's picture

welcome to the human race.  

-snake plissken

Boris Alatovkrap's picture

"That's it man, game over man, game over."

- Marine in Aliens

Inthemix96's picture

The idiots have taken over the asylumn.

And black is white.

Jekyll_n_Hyde_Island's picture

"Small issues – a marginal residential development in Scottsdale, a deal by Greek monks for some Athenian commercial real estate – quickly cascade to become the tornado in Texas."

  Hindsight is 20/20.

A biologist studying one type of butterfly isn't going to understand the flapping of a different species' wings.

DSGE modeling and Hedge, these are the rotational magnetic gravities that will propel our global economic axis the next 10 years.

  Chaos theory is for people who haven't graduated to quantum theory.

ToNYC's picture

Quantum Theory is for those who don't know a wave from a particle and crowd all my measurements with their stinking vectors penetrating my space reducing my uncertainty to zero about you, math separatists void suckers all.

Boris Alatovkrap's picture

Quantum Theory of Banking... cannot know where dollar is and how much is worth at same time. Same theory is apply to shell game. Same is thing!

ZerOhead's picture

The sociopaths have taken over the government.

And wrong is right.

Joe Davola's picture

Interesting "recommended" article showed up from the one you referenced:




Lowering the denominator - heh.

NotApplicable's picture

YOUR government was taken over by sociopaths long, long before you were born.

Question is, why do you still support the beast by claiming ownership of it?

ZerOhead's picture

'THE' government is not 'MY' government any more than it's anyone's government other than 'THEIR' government.

Still you have to throw a couple of ducats at it every now and then to just to keep the dogs at bay...


HD's picture

I wish I had read this before I cloned all those dinosaurs...

TheMayor's picture

One of the most informative ZH articles ever.

TheMayor's picture

Apparently some people didn't like the extra reading assignment at the end of the article.


Nonetheless, great article for exposing a whole new audience to chaos theory.

Taint Boil's picture




Reminds me of  Overbar transcription error:

The most expensive hyphen in history

The error had occurred when a symbol was being transcribed by hand in the specification for the guidance program. The writer missed the superscript bar (or overlineby which was meant "the nth smoothed value of the time derivative of a radius R". Without the smoothing function indicated by the bar, the program treated normal minor variations of velocity as if they were serious, causing spurious corrections that sent the rocket off course. It was then destroyed by the Range Safety Officer

[Bottom of page]




Going Loco's picture

This article makes you realise just how naff all that Pheoneix, Grant, Testosterone, etc. offal is. Kudos to ZH. One great article a week is enough to keep the pot boiling.

Major Major Major's picture

zn+1 = zn2 + c, Bitches

ParkAveFlasher's picture

It's a big club, you ain't in it.  Slainte.

Headbanger's picture

And let's not forget what is perhaps the best corollary to Chaos Theory:  Murphy's Law

"Anything that can go wrong will. And at the worst possible moment"

Dr. Engali's picture

Morpheus : This is a sparring program, similar to the programmed reality

of the Matrix. It has the same basic rules, rules like

gravity. What you must learn is that these rules are no

different than the rules of a computer system...some of them

can can be bent. Others...can be broken. Understand?



g speed's picture

so true---lie about the butterfly and lie about the outcome-- its really not real--

IndicaTive's picture

When you're invited to shoot pool on someone else's table for the first time, keep your money in your pocket. 

HD's picture

and keep your eye on their balls...

IridiumRebel's picture

in 50 yrs we will probably have some distopian nightmare and a helluva lot less people. 

ZerOhead's picture

10 or less.

Food aid to Africa/India/China when TSHTF anyone?

Remember this? > http://www.ft.com/cms/s/0/485c93ae-a06f-11df-a669-00144feabdc0.html#axzz...

buzzsaw99's picture

"Markets" seem like chaos but only because they are micromanaged to appear that way.

Mark_BC's picture

Economics is not in any way science. Most people and almost all economists seem to think that science is about applying big complex mathematics to describe things. That is not what science is. Science is simply an approach to the world which says that "You are trying to convinve me that this thing behaves according to this principle? Then Prove it! And I won't believe it until I've seen years and years of rigorous hypothesis testing which is unable to disprove the hypothesis".

That's all science is. It's formulating hypotheses and then performing rigorous attacks on them to see if those hypotheses can hold up. If they can continue to be un-disproven (they can never actually be proven, only un-disproven) after several years of this scientific method then they are elevated to the ranks of "scientific theory".

Then, economists come along and think that because they can apply the same sorts of complex mthematics and pretty charts that scientists use, then their "theories" (in actuality, economic "theories" are nothing more than hypotheses) can be scientific too!

Economics is not a dismal science, because it isn't a science at all. Unfortunetely, however, the average person doesn't understand the distinction and this is very unfortunate because when the economic system collapses people are going to (rightly) blame it on the academic economists, and then (wrongly) lump scientists in with them. Economics is the laughing stock of the academic world, it is tarnishing everything to to with higher education, it is a total sham. Yet this farce of a discipline is also the one that has free reign over our societies.

akak's picture















Which one does not belong in the list?


web bot's picture

ROFL... Let me guess...

NotApplicable's picture

Your point would've been better made by using Keynes.

Tinky's picture

The answer is "Krugman", which you misspelled. It should have read "Klugman", as in Jack.

Citxmech's picture

Somewhere, Karl Popper just smiled.

ReactionToClosedMinds's picture

not bad Mark_BC  .... and I am no 'academic lover' but think you sum it up well, at least for ecnomics.


  1. to some material degree ..... economics is really 'behavioral' ... hence inherently unpredictable.   All the formulas and graphs can only go so far to hide this elemental fact.  So to is finance & business ... where 'marketing' and more so 'sales' ...are extremely 'behavioral' while accounting is more 'measurement' and 'control' (where's the beef?) directed.
  2. But even the 'hard' or 'physical' sciences are not immune to 'behavioral' biases.     Look at how long it took for the 'measurement problem' in quantum theory to be openly & honestly addressed ...once the inherent limitation of 'FAPP' [For All Practical Purposes ..... which is akin to ..... in the long run we are all dead] was acknowledged.  Einstein never bought into FAPP while appreciating its 'practicality'.  How can one 'do good physics' when you dismiss anything with FAPP?
Mark_BC's picture

Yeah I agree ReactionToClose, there are limits to what science can do. Regarding Point 2, that "measurement problem" is a critical idea regarding the scientific method, and a perfect example of why science can never prove anything, it can only non-disprove things. If the world had "proven" the validity of Newtonian or Einsteinian mechanics then there would have been no room left for quantum mechanics. But if science merely un-disproved Einsteinian and Newtonian mechanics then that leaves open tons of opportunity for other explanations of the world to be developed, that are applicable to size and time scales that Newton and Einstein didn't encompass.

ZerOhead's picture

Back in the Bronze ages and before, it was the the prophets, oracles and associated fortune tellers that used to be the economists of the day.

Just like today you would be amazed at what you can predict with a bucket-full of goat entrails...

thelibcentury's picture

Your logic is weird.

You argue that economics is not a science at all, and associate this with the premise that modern economists have foolishly pursued complex mathematics as a means to achieving the scientific end, but then you state (correctly I would add) that this is not what science truly is.

So in that case, why is economics not a science? I don't see the connections you are making?


In my opinion, economics definitely is a science - not one like physics in the sense of precise mathematical equations, but as a rational study of human behavior along with a development of certain key laws, based on exactly your definition of science:

"It's formulating hypotheses and then performing rigorous attacks on them to see if those hypotheses can hold up."


It might just be me, but I find it an invalid argument.

Mark_BC's picture

But economists do not engage in the scientific method. They don't postulate hypotheses and then subject them to years of attack using observable evidence, controlling the methods to factor out unrelated inputs. It seems they take some simple hard rules like supply and demand, and then expand on these basied on political ideology to develop all of their more complex models (taken to the extreme with Keynesian economics). This is why, today, you can find just about any economic "theory" being flogged by someone, all the way from radical right wing anarchists to left wing communists. And all purport to be more accurate in how their particular beliefs represent the real world. The problem is, none of them do, otherwise the evidence would weed out the invalid economic principles. You'd never see such a wide divergence in beliefs in science. 

The problem is economics can't go through a formal scientific method because it is our economies and societies that would be the guinea pigs. And the experiment would have to span more than 50 years to get any really meaningful data, since this is the length of time the US dollar has been the global reserve currency which would grossly skew any results obtained from observing how economies react to certain policies. Plus the world is running out of energy so that, over 50 years, would be an uncontrollable factor that could no be isolated. Economics is not predicatable.

Diogenes's picture

You are right it is not practical to carry out 50 year experiments comparing different economic or political systems. This is where history comes in. Nearly everything has been tried at one time or another. History can help figure out the cause/effect of different policies.

IndyPat's picture

Except that we...humans...write history.
And we lie. A lot.