Models: Does Elon Musk Exist?
What pet elephants teach us about the stock market.
Re-Assembling Reality #26a. By Mike Brownnutt and David A. Palmer
Models are ubiquitous in science: Epidemiologists make models of viruses spreading. Physicists make models of electrons moving through metals. Neurologists make models of brain activity. Engineers make models of building structures.
If the models are any good, they tell us something useful about pandemics, or conductivity. They allow us to make predictions about what a person may do, or when a building will collapse.
In this essay we will consider what can (and importantly what cannot) be said about the things which are included and excluded from models.
Basic logic
We like to imagine scientists as submitting themselves to the constraints of basic logic. We shall therefore start this essay with a little basic logic. Later we shall see what happens when such logic is applied to models, and we shall see just how uncomfortable things can get.
Consider, first, a simple logical statement:
If my pet is an elephant,
then my pet has four legs.
I have a pet. I take a look at my pet. I make an observation.
My pet has four legs.
What can I conclude? Is my pet an elephant? No idea! Based on the available information, my pet might be an elephant. Or it might be a cat, a dog, a stegosaurus, or a guinea pig. I certainly cannot say that my pet is definitely an elephant. I cannot even say that my pet is probably an elephant. It may be that further investigation into ownership of quadrupedal pets shows that, all other things being equal, even if my pet has four legs, then it is still probably not an elephant.
I can argue from elephant-hood to four-legged-ness. Attempting to argue back from four-legged-ness to elephant hood is a logical fallacy of a type which logicians call ‘affirming the consequent.’
Basic gas laws
Few scientists would get into much trouble with questions about house pets. But let us consider something that looks more like science. Consider the relationship between a gas’ pressure (P), its volume (V) and its temperature (T). It can be shown, using an atomic model of gasses, that
If a gas is made of atoms which are point particles
then PV/T is a constant.
I take a look at my gas. I make an observation.
PV/T is a constant therefore…
What can I conclude?
I cannot conclude a whole lot:
— I cannot conclude that atoms are point particles.
— I cannot conclude that atoms are probably point particles.
— I cannot conclude that atoms are something like point particles.
In case it is unclear why we cannot draw such conclusions, consider the following conclusions (which we also cannot draw):
— My guinea pig is an elephant.
— My guinea pig is probably an elephant.
— My guinea pig is something like an elephant.
The final point may seem promising, because my guinea pig is like an elephant inasmuch as it has four legs. But let us scratch below the surface: is there any other characteristic that my guinea pig necessarily shares with an elephant, beyond the one stated in the original syllogism? No. A chair also has four legs. Two flamingos have four legs. The similarities necessarily shared by all things with four legs stops at four-legged-ness.
If you catch a scientist unawares and press for a quick response to the limited conclusions we can draw about gasses, they may offer a slight fudge, grasping in the moment for what looks like a get-out clause:
“Well, of course. You see, if you measured your gas more precisely you would find that PV/T is not exactly a constant. And so this shows that the atoms are not exactly point particles.”
This, however, ducks the issue. The question is not what we should conclude if and when PV/T turns out to not actually be constant. Rather, we are imagining a world in which we found a gas that had a constant value of PV/T, and we could show that this held constant with perfect precision under all measurement conditions. And in that world, logic would still not let us conclude that such a gas was made of point particles.
This feels, intuitively, somehow wrong. How can we have gone to all that effort and measured P, V, and T to infinite precision, and still not be able to say that the gas is made of point particles? What else could it possibly be made of?
Unfortunately, no matter how much our intuition may object, no matter how fruitless our attempts are to find an alternative explanation for the observed behavior, the logical formalism remains resolute. We can say, “If I assume that my gas is made of point-particle-like atoms, then I get reasonable predictions regarding the relationship between pressure, volume, and temperature.” But we cannot say (with any logical support) that, “If PV/T is a constant, then my gas is made of point particles.” Cannot.
This example is, of course, trivial. The further we move from simplistic toy examples, the stronger our intuition gets that a fruitful model really should allow us to say something about the underlying system being modeled. To help disabuse ourselves of this view, let us turn to a truly complex system.
Modelling markets
It is hard to see atoms. It is much easier to see people.
A person makes a widget that I want to buy, and I buy it. If lots of people want to buy similar widgets, the person may start a company and employ thousands of other people so that they can mass-produce widgets. If the widget is complex to manufacture, the company may become part of a larger supply chain: one company mines the raw materials, another refines the materials, another makes them into components. Another company assembles the components into widgets, another buys the widgets to sell to a company that puts widgets into some piece of equipment that another company then sells to me.
Maybe one day a new company comes along which can outsource its labour and make widgets more cheaply. Maybe the government raises interest rates so that I would rather save my money instead of spending it on widgets. Maybe a war breaks out and the cost of raw materials goes through the roof. Maybe a pandemic breaks out and everything in the entire world gets turned upside down.
Surely markets— being subject to so many different factors — should qualify as complex systems. Let us take the stock market as an easily-quantifiable example. We might expect a simplistic model of markets that only takes one piece — say, consumer demand — into account to miss key aspects of what is happening, and poorly account for a stock’s price action. We would anticipate, however, that the model would be improved by making it more accurately reflect the complexity of what is really happening. Once sufficient detail had been added to the model that it well-reflected the price action in the market, we might have some reasonable confidence that our model had included the things that were important, and that anything which our model excluded was not important.
This seems intuitively reasonable: if a pandemic influences the market, how could we model markets without reference to pandemics? And if we can model a market without reference to pandemics, how can anyone claim that pandemics effect the market?
Let us formalise this, put it to the test, and see where it leads.
Setting up the question
If products, supply chains, government interventions, and pandemics have no effects on markets,
then I can model markets without reference to products, supply chains, government interventions, or pandemics.
So let us look at a market and see what happens: can I model markets without reference to products, supply chains, government interventions or pandemics?
Here is a chart showing the price of a particular company’s shares. I won’t say which company because, frankly, if I am going to model the share price without reference to products, it seems appropriate to not even know what company it is. Maybe the company makes glass ornaments. Maybe it sells tanks. I don’t care. [1]
The horizontal axis shows time. I won’t say how much time because, if we are really going to model the company without reference to context, the time scale should not matter. If the price goes down because of a global recession, that will take months, not minutes. If the price goes down because someone got bored on a Friday afternoon and dumped their holding, that will take minutes, not months. And if the price action is unrelated to any of these triggers, we do not care what timescale we are looking at: a global recession and a slow Friday afternoon should look the same.
The vertical axis shows the price of the shares. I won’t say how much they cost because, if we are going to model the company without reference to context, the actual price should not matter. Sure, when you buy a product like a toaster, it matters whether you are buying it for a dollar or a thousand dollars. But stocks are not products. And products (in our context-free model) do not matter.
Can we model this with the help of context?
Having established what the chart is showing, we can turn to analysis. But before we attempt to model the company without reference to the context, indulge me for a moment: is there anything obviously helpful to be seen when we do consider the usual economic mundanities like products and government interventions? Without spoiling the mystery and revealing exact products or time-frames, let us look at the direct impact of some potentially significant events.
The basic trend is up which, as markets go, seems like good news. Maybe the share price is going up because this is an innovative company that is doing really well and bringing new products to market.
The arrow labeled (1) shows when the first major product in the time-frame under consideration was released. Presumably it was well received, because the share price went up for a while (before going down a bit, then up, then down, then up; presumably for reasons unrelated to product releases). I guess product (2) was a bit of a damp squib, because the share price just went sideways for a while. Or maybe it was great because it stopped the share price from going down. Product (3) was apparently a slow burner because the share price went down for a bit until everyone realized how good the product was and the price went up. Either that, or the share price and share-price movements are unrelated to the products the company sells.
Maybe this is no surprise. New product ranges are less important for a business than money: making a profit on an old product is better than making a loss on a new one. So let’s look at the impact of earnings instead.
Green arrows show various times when a financial report was released and reported earnings were higher than expected. Red arrows show reports with earnings lower than expected. One might imagine that when people are told that the company is making more money than they had previously thought, the share price would go up, to take the new information into account. This happened for the cases marked (1). Similarly, when people find out the company is making less money than they had previously thought, the share price should go down, to take the new information into account. This happened for the case marked (2). It looks a little strange that the jumps up at (1) and the jump down for (2) are all the same size, but we will park that puzzle for the moment and return to it later, because we have more pressing problems.
Our first pressing problem occurs at (3) where the company beat expectations, the share price jumped up by the expected amount, but then crash down immediately afterwards. This seems odd. Similarly odd is when the company missed expectations, had the share price jump down the expected amount, but then had it start to head straight upwards again (4). And if such responses to earnings reports seem strange, consider the ‘non-responses’ to earnings reports: why would the company beat expectations but have the share price keep plodding down immediately afterwards (5), or miss expectations but have the share price keep heading up (6) like nothing had changed?
Maybe the company’s earnings are not as important as one might initially have thought.
What else might there be? Maybe there are macro-economic factors at play. The Federal Reserve System (“The Fed”) gets a lot of press for the role it (allegedly) plays in the US economy. (Yes, the company we are analysing is based in the US though, as we shall see, that fact will be utterly irrelevant for our context-free modelling). There is a common narrative touted by people who think that it is relevant, in understanding markets, to consider things like Central Banks, and monetary policy, and how much money people have. In this narrative, when The Fed raises interest rates, people spend less, companies cannot grow so fast, and so the share price should go down.
Let’s look at what happens in practice for this company when The Fed changes interest rates.
Arrows pointing upwards show when The Fed increased interest rates. Arrows pointing down show when The Fed reduced interest rates. Arrow (1) shows interest rates go up and the share price go down, just like it should. The arrows marked (2) show interest rates go down and the share price go up, just like it should. Arrow (3) shows interest rates go up and shares go sideways. The arrows marked (4) show interest rates go up and share prices go up. Arrow (5) shows interest rates go down and share prices go down. So overall… um… I’m going to call this a mixed bag. It is hard, based on this data, to draw a solid link between the actions of the Federal Reserve and this company’s share-price action.
Our intuition said that a simplistic model of markets that only took one piece into account might miss key aspects of what is happening, but that the model would be improved by making it more accurately reflect the complexity of what is really going on. Maybe, then, we can get a better picture by combining everything together. Can we account for what we see by considering the combined effects of product development, earnings, monetary policy, and whatever else is going on in the world?
Let us tell a story:
The company missed earnings expectations (1) so the price went down. But then they released a new product (2) and people liked it, so the price went up. They beat earnings expectations (5) so the price went up even more. But then the pandemic happened (6) and the whole world stopped, so the price went down until The Fed stepped in (7) and reduced interest rates so the price went up. At some point (8) the company released a new product that people didn’t really like so the price went down. Until the company beat expectations on earnings anyway (9) so the price went up.
As we add more and more layers, we feel like we can start to tell a story that seems reasonable. Admittedly, there are some bits that still don’t make sense — like why the price went up at (3) when interest rates were increased, and why they went down at (4) when interest rates were reduced. And we haven’t even attempted to address questions of all the minor wiggles along the way. But maybe if we added enough extra factors of complexity we could work those out. And — fortunately for us — however much we add, if things still don’t fit, we can always invoke “other unknown factors.”
Unfortunately, even with all the complexity, it is hard to make solid predictions. It is obvious after the event that a pandemic will send stocks tumbling; but you can’t predict pandemics. And even once you see things tumbling, quantitative predictions are tricky: how can you possibly know how far it will fall? And (illegal insider trading notwithstanding) how can you know exactly when The Fed will come in and save the day? [2]
So this is how far our modeling takes us: if we take products, supply chains, government interventions, and pandemics into account, we get a complex, messy model which is full of holes and which is better at providing explanations after the fact than it is at making proper quantifiable predictions. But hey, what else can we do?
Blue lines and context-free modelling
This is what else we can do: We can face the fact that keeping track of products, earnings, government interventions, or pandemics is hard. And it is much easier (and frankly much better) to model the stock market without reference to any of them. Welcome to context-free modelling.
The theory is very simple: the entire stock market is ruled by blue lines.
Who cares if there is a pandemic, or a war, or a recession? It does not matter. At least, not to the stock market. They are of no relevance. Products and pandemics, federal policy and foreign invasions: they have no impact on the stock market whatsoever. Because the stock market is ruled by blue lines. Wars, pandemics, and recessions are powerless against the effects of blue lines.
There are two main blue lines governing the stock we are considering here, and they help to answer a lot of questions.
After the share price fell at (1), why did it stop falling and start to go up again? It had nothing to do with a product release at (2). That was just co-incidence. The share price stopped falling because it hit a blue line.
The Fed raised interest rates at (3), but obviously the stock couldn’t go down; it had to go up because of the blue line. And The Fed lowered interest rates at (4), but obviously the stock couldn’t go up; it had to go down because of the blue line. Demonstrably, the actions of The Fed are nothing compared to the power of blue lines.
Do not believe the people who tell you that the price went up at (5) because of a better-than-expected earnings report, or crashed at (6) because of a pandemic, or kept dropping like a stone until The Fed stepped in at (7). Such tales are just-so stories for children. The truth — which allows quantitative predictions — is that the price went up until it hit the upper blue line, fell until it hit the lower blue line, and then started going back up again. Because that’s how stocks work; and that’s what blue lines do.
And now we can see what was happening at (8) and (9). The rally had already started by the time the earnings report came out. So we can reject out of hand the idea that earnings caused the rally. No: the stock went up because it had reached the lower blue line and had to go up.
As we delve deeper into the model we notice that there are secondary blue lines, spaced equidistantly between the main ones.
We wondered earlier why the drops after the company missed earnings expectations were all the same size. The arrows marked (1) make the answer clear: the price was dropping down from one blue line to the next. And why were the jumps after the company beat earnings expectations all the same size? Look at the arrows marked (2): the price jumped up from one blue line to the next.
And why did the share price drop exactly the amount it did just before The Fed dropped interest rates (3)? Look at the blue lines. And when the company missed earnings but the price kept going up (4), we can not only say why the price went up, but also why it carried on going up at the rate that it did: it was working its way along a blue line.
Why stop here? We can delve even deeper.
If context doesn’t matter then, as we said at the start of this essay, the time scale shouldn’t matter and the absolute price shouldn’t matter. The chart we have been looking at so far covers five years of time and a factor of three hundred and fifty in share price (shown here on a logarithmic scale). But if we zoom in, we find that even on much shorter timescales and much smaller price fluctuations, blue lines still rule.
At the very end of the chart we have been looking at, there is a jump in share price which (as we know) was not caused by an earnings report, but was caused by blue lines. And then the price moves gently up and to the right, following along the blue line. On the face of it, there is not much going on after that jump: the share price just works its way up along the blue line. But when we zoom in we see, in a beautifully fractal manner, the price is not a smooth walk up, but again bounces between blue lines.
Having hit a major blue line at (1) the price bounces between blue lines until (2), when it finally falls all the way to be supported by a major blue line at (3). (Although I say “major blue line”, these lines are so close that they could not even be resolved on the main chart.) After volatile trading in which the price bounced off the higher blue line, shares end the day a fraction higher, but still sitting on the blue line at (4). Within an hour of markets opening the next day, it has shot up two blue lines (5), but is stopped from going much higher the next day by the next major blue line (6).
If we chose, we could keep zooming: one week per bar, one day per bar, one hour, one minute… the patterns would look the same. And this is not just the case for the nature of bouncing between blue lines. Consider the shape of the dips:
The dip shown in circle (1) took four months to play out. Peak to trough, it wiped $5 billion (65%) from the company’s market capitalization. Some people would have you believe that the rise, fall, and recovery were due (respectively) to unexpected record earnings, an unforeseeable pandemic that shut down the world, and the heroic intervention of The Federal Reserve.
In contrast to such a story, context-free modelling says it was entirely predictable, and due to blue lines.
When we zoom in, the dip in circle (2) took four days to play out, and dented the company’s market capitalization by only 6%. Some people would have you believe that, however similar this looks to the dip in circle (1), it must have been caused by something else. They might not know what caused it, because there didn’t seem to be a whole lot going on at the time. But, whatever it was, it wasn’t a pandemic and a global recovery spurred on by government interventions, firstly because such things were not happening at that time and then because, even if they had been, that kind of thing just cannot play out in four days. The similarity in shape between the two dips (they will say) is strange — possibly even inexplicable — but certainly just co-incidental.
In contrast to such a story, context-free modelling says the two dips look similar because they were caused by exactly the same things: blue lines.
Blue lines. Blue lines everywhere
It must be stressed that this example is not some cherry-picked case where the company is exceptionally well insulated from the outside world. The company is actually Enphase. They are based in California, and they design and manufacture solar-based home-energy systems. One can reasonably assume they get hit by all the usual things that might buffet such a company: a new CEO; the outsourcing of work to India; the rise, fall, and rise again of the Green New Deal; the passing of the baton between US presidents who have contrasting views on climate change… Not, of course, that you could guess when any of those events happened from looking at the chart.
Still, you have probably never heard of Enphase. Let’s look at a company you have heard of. A company that stands in the glare of intense media interest and high-profile news stories. Surely the predictability afforded by blue lines must come to nothing against the loose-cannon which is Elon Musk’s Twitter account. Tesla, of all companies, surely defies expectation.
In 2021, Tesla shares had been on a seemingly unstoppable tear. In the six months leading to November, the share price had more than doubled. Then, on 6th November 2021, Elon Musk (Tesla’s CEO, and largest shareholder) put out a Twitter poll asking if he should sell 10% of his stake in the company. He promised to abide by the result. When the results came in, 58% of the 3.5 million votes cast said that the world’s richest man should sell.
The shock possibility of Musk wanting to dump $25 billion worth of Tesla shares (and affirmation that the company is being run by a CEO who is so reckless as to let Twitter decide such things for him) sent Tesla’s share price into a tailspin. On Friday 4th November, the last trading day before the poll, the share price stood at $1,208. By the Tuesday following the poll, the share price had fallen over 16%, wiping almost $200 billion from the company’s market capitalization. Since then, nothing could bring the share price back up. There was a stream of great news about the company: record earnings and margins that smashed expectations; record-breaking sales growth, even at a time when every other car manufacturer was struggling with chip shortages, supply-chain issues, pandemics, and wars; existing Tesla factories were making cars at rates never thought possible, and new factories were being brought online. But nothing could revive the stock. At best, the stock sometimes managed the briefest of relief rallies before slumping back to a seemingly unstoppable downward trend. Four months after the fateful poll, the share price was down 25%, hovering around a mere $900.
No company can work with that level of unpredictability, and Musk is as unpredictable as they come. Clearly, the self-proclaimed Techno-King of Tesla must get control of his Twitter-finger before he destroys the company.
At least, that is the story told by people who appeal to complex explanations where products and sales and agency and people matter. But we have a model which, frankly, works a lot better than trying to guess what Elon will tweet next. And it involves blue lines.
The stock price had been working its way up a blue line until it dropped from there (1) to the base blue line (2). It then climbed until it hit the top blue line (3) before rebounding back towards the bottom blue line (because that’s what happens to share prices when they hit the top blue line). It climbed again to hit the top blue line (5) before rebounding again and settling on the bottom blue line (6). As explanations go, that is about as straight forward as they come.
I confess I do not know why the pandemic (if you believe in the pandemic) happened to start at (1), or why The Fed (if you believe in The Fed) should have taken action to reduce interest rates at the same time as the base blue line stopped the share price from falling (2). There are those who think that the share price shot up just before (3) due to reports of record vehicle deliveries. And others who claim the share price collapsed just after (3) because the market became more cautious about growth-dependent valuations. How vehicle delivery reports are timed so perfectly to the requirements of the blue lines, I do not know. I also do not know what motivated Elon Musk (if you believe in Elon Musk) to send out a Tweet (if you believe in Twitter) at exactly the right moment (5) for Twitter to take the credit for influencing the stock market, rather than the credit unambiguously going to the blue lines.
Despite all of these things which I do not know, here is something I do know: a model based on blue lines is much better at predicting the actions of share prices than a model which attempts to second guess what Elon Musk will Tweet next.
What can we conclude about markets?
At the start of this essay, we noted that, even if a model reliably — even perfectly — predicts the behaviour of a system, logic does not allow us to conclude anything about the nature of the underlying system, beyond the fact that the model reliably predicts its behaviour. Moreover, just because a fruitful model includes or excludes certain elements, we cannot conclude that the system being modeled includes or excludes those elements, or that those elements do or do not play a meaningful — and even causal — role in the process being modeled.
Recapping the example with which we started, it may be the case that a gas made of point-like atoms would obey a certain law. And it may be the case that the gas under consideration obeys that law. But we cannot therefore conclude that the gas under consideration is made of point-like atoms, or even of anything resembling point-like atoms.
Logic notwithstanding, we also noted at the start of this essay that our intuition tells us that fruitful models really should allow us to say something about the underlying system being modeled. Moreover, the more complex the system, the stronger our intuition on this point becomes. We desperately want out models to be able to say something more. How could it possibly be that a model would work if it invokes fictions, while ignoring the mechanisms actually at play?
So we selected a complex system — markets — and set up a syllogism:
If products, supply chains, government interventions, and pandemics have no effects on markets,
then I can model markets without reference to products, supply chains, government interventions, or pandemics.
Then we took a look at markets and made an observation:
I can model markets without reference to products, supply chains, government interventions, or pandemics.
I really can. I can model them very well. I can model them quantitatively. I can model them across different timescales, valuations, and sectors. I can make solid predictions, and these predictions get borne out.[3]
I might from this be tempted to say (as many people have long argued) that the stock market is a fix. Or that, for all their noise and bluster, governments and central banks achieve nothing. Or that the pandemic is a hoax. Or that the electric car market would be the same, with or without Elon Musk.
But, however much my model does not need to invoke them, I cannot logically use their absence from my successful model of the market to claim that such things do not, in fact, have any effects on the market. This would logically be up there with claiming that my pet is an elephant just because it has four legs.
Models and ontology
Before leaving markets, however, let us take one final step further into absurdity. Consider the following syllogism:
If products, supply chains, government interventions, and pandemics do not exist,
then I can model markets without reference to products, supply chains, government interventions, or pandemics.
I take a look at the markets and I find,
I can model markets without reference to products, supply chains, government interventions, or pandemics.
Can I from this conclude that (more than simply having no effect on markets) it is the case that products, supply chains, government interventions and pandemics do not exist?
No, I cannot!
— Is it surprising that believers in Elon Musk claim that he sent out a controversial Tweet on the exact same day that my model said Tesla stocks would plummet? Yes.
— Can I explain why the two should coincide so perfectly? No.
— Should I, from this, conclude that Elon Musk does not exist? No.
—What would have happened if Musk had never sent the Tweet? I don’t know.
—Can I say that blue lines are more likely to exist than Elon Musk? No.
— Can I insist that Elon Musk and his Tweets, if they can be said to ‘exist’ at all, are nothing but epiphenomena that emerge out of the activity of blue lines? Absolutely not!
— Am I irrational or unreasonable for continuing to believe in Elon Musk, even though I am unable to explain why alternative models work so well, or even better, than the ‘Elon did it’ model? No
Such is the nature of models.
Models can be exceptionally powerful. They can be exceptionally effective at predicting the behaviour of a system. But they cannot be used to justify claims about the nature of the system being modeled [4].
Exercising restraint in this regard is very difficult. Models often look so good, so powerful, that it is hard to override our intuition that they must be telling us something deep. Maybe you have enough restraint to accept that Elon Musk exists, even if blue lines provide a good model for Tesla’s price action.
In the next essay, we will look at free will and divine action. In these areas, the restraint required in light of the limitations of models plays out in some truly uncomfortable ways.
Disclaimer
Nothing in this essay should be construed as financial advice. If you take up trading and your life falls apart because you lose lots of money, it was not me that made you do it. If you take up trading and your life falls apart because you gain lots of money, it was not me that made you do it. If you take up trading and things go OK and you live out your days in comfort, please do not imagine that just because something happens to be a reliable way of making money it is for that reason not an moral abomination or a blight on humanity.
Footnotes
[1] In getting feedback on this essay, one comment was that this paragraph about not caring what a company makes made no sense. Obviously it matters what a company makes: companies that make glass ornaments do badly when war breaks out, and companies that sell tanks do well. But such an objection already assumes something that we are setting out to question: that wars make a difference. If context doesn’t matter — if wars don’t make a difference to the stock market — then it doesn’t matter whether a company is making tanks or ornaments. Such is the logic of the model being presented in this section.
[2] For what it is worth, Modern Portfolio Theory (MPT) states that the answer to these rhetorical questions is simple: you cannot. MPT says that there is no way to predict the stock market, because that would let you beat the market, and there is no way (according to MPT) to consistently beat the market. Unfortunately, Warren Buffett didn’t know that so, over the past six decades, he has beaten the market by 50,000%. MPT’s models say that Warren Buffett cannot exist. By the time you have read this essay, you will know what conclusions we can draw from such models.
[3] I confess that, strictly, all of the statements made in this essay have been post-dictions. They are pretty pictures I posted on a blog after the event. But others have made pre-dictions, and have been doing so for decades. As you might expect, if you can predict the stock market there is money to be made. And if there is money to be made, a lot of people get very interested. Modern technical market analysis in the US was pioneered by people like Richard Schabacker (Technical Analysis and Stock Market Profits, Harriman House Ltd. 2005. First published in 1932) and Robert D. Edwards, John Magee, and W. H. C. Bassetti (Technical Analysis of Stock Trends, CRC Press. 2021. First published in 1948). Since then, technical analysis of markets has grown to become its own discipline within economics, spawning other disciplines on the way, such as behavioral finance. And the predictions work well enough for some people to get crazy rich, regardless of what Modern Portfolio Theory says.
[4] If you have been following this series of Essays, this result may look a lot like Kant’s claims about the relationship between phenomena and noumena, which we first discussed in Essay #13. The derivation of the result in this Essay is quite independent of Kant’s, but the conclusion is one with which Kant would probably have been very comfortable.
