Schrodinger's Economics: Getting Ready for the Impending Quantum Revolution in Thinking

Predictions are messy, forecasting is heinous, and our brain plays massive tricks on us when we try to objectively interpret model results; but what if we made predictions in the same fashion that the brain makes decisions, assuages emotions, or evaluates risk? Our theorized quantum reality is best explained with a quantum framework. Since Schrodinger’s economics is still far away and most economists grow queasy at the thought of sullying their pristine social science, paling at the thought of either physics or humanism muddying the waters, maybe we can use computer science as a tool and artificial neural networks as the medium to backdoor a quantum revolution. Researchers from the Trinity College of Dublin have made two groundbreaking conclusions that provide steel for my heretical conjecture: "Quantum mechanisms are at work in sensory systems feeding the brain with information", and "Beyond those sensory inputs, more complex brain functionalities depend on the presence of specific nuclear spins". The current false dichotomy between economics as a quantitative and social science is a hindrance to societal progress. If our brain thinks in a quantum nature, where things exist in a slippery superposition, how can the study of people’s emergent actions in the face of scarcity definitively be either qualitative or quantitative? Economics is neither a quantitative discipline nor a qualitative study of people; it is inherently a study of both. Quantum thinking will allow us to model humanistic, compassionate, and empathetic behavior mathematically. The article will explore how we can use the structure, complexity, and evolutionary-tuned efficiency of artificial neural pathways to unify economics.

The brain is a complex behemoth in form and function. We know enough to know that we know so little about how the brain works. In fact, "whether those or other macroscopic systems in the brain can be non-classical is still unknown". Experimental methods, which could distinguish classical from quantum correlations in the living brain, haven’t yet been established, meaning we haven’t yet done the research or don’t possess the means to truly understand the hidden mechanisms behind the aggregate propagation of charges along myelinated neurons that ultimately form our core thought patterns, ego, and ideals. Despite not knowing with true certainty if our higher thought processes and decisions happen in a quantum fashion, given that we at least know our sensory information seems to be processed quantumly, a quantum framework should still be more accurate than a classical one. Let’s think about this intuitively. The brain has an incalculable number of sensory inputs at any given time. We honestly should pat ourselves on the back every time we make any decision, let alone complex value judgments or risk evaluations. Our brain processes untold petabytes of data to fuel our broken cognition; even if this structure isn’t truly or wholly quantum, I posit that human cognition is an erstwhile approximation of our quantum reality, one that better captures the inherent complexity in the sheer size and breadth of data we continually churn through to make thoughtful decisions.

Now that the brain’s status as an esoteric quantum computer has been established, how can we leverage its qualities to change economics? Since true-to-life renderings of human thinking would take more computer power than we have available on earth, perhaps we can use quantum thinking merged with algorithmic thinking to lighten the load on our poor GPUs and CPUs. An algorithm, abstracted from its manifold uses, is a quite inelegant and unsophisticated method of guessing and checking. In essence, algorithmic thinking, without machine learning modifications, is the dumb brute method of borrowing computing power to guess all possible solutions to a complex problem, with the goal of figuring out which of those many guesses is the most optimal for our goal. The biggest limitation in non-ML algorithms is that they execute their search for the most optimal solutions in the same pattern we, the user, give them. Bluntly, it’s dumb as a brick and has no reflexivity, simply regurgitating the pattern of search we provide without learning from each successive guess to improve the model. Machine learning introduces dynamism, where we can brute force an algorithm to make guesses but have it learn from each guess at some rate and method we define. Imagine we took this wonder one step further, using this smart guessing or machine learning-enabled brute-force capability beyond just minimizing root mean squared error in regressions. We can apply this same level of iterative, smart, algorithmic thinking to a structure that mimics the quantum information processing capabilities of the brain, giving us something that ought to be startlingly close to reality. Let’s see one potential application of the power and drawbacks of this thinking implemented in a real-life financial example, using S&P 500 prices. The resulting code is hardly robust. It lacks forward validity, and the snippet below is meaningless due to my inexperience with computer science; when run fully, it will throw an index error when trying to reshape the test data after running for 100 epochs; however, running the model helped me understand the intuition behind how such a model could be incredibly powerful if tweaked.

import math
import pandas_datareader as web
import matplotlib
import numpy as np
import pandas as pd
from sklearn.preprocessing import MinMaxScaler
from keras.models import Sequential
from keras.layers import Dense, LSTM
import matplotlib.pyplot as plt
import yfinance as yfin
plt.style.use('fivethirtyeight')

# Import S&P500 historical prices
yfin.pdr_override()
S&P_Index = web.get_data_alphavantage("SPY", api_key="Key")

# Find number of rows and columns in the dataset

 (3673, 5)- 3673 rows and 5 columns

# Visualizing closing price history
plt.figure(figsize=(16, 8))
plt.title('Close Price History')
plt.plot(S&P500_Index['close'])
plt.xlabel('Date', fontsize=18)
plt.ylabel('Close Price USD', fontsize=18)
#plt.show()

# Filtering for just the close column in the S&P dataset
data = S&P_Index.filter(['close'])

# Converting from our data from pandas df to a numpy array
dataset = data.values

# Setting up training data

training_data_len = math.ceil((len(dataset) * 8))

print(training_data_len)

# training data has length of 29385

# scaling our data

scaler = MinMaxScaler(feature_range=(0,1))
scaled_data = scaler.fit_transform(dataset)

# creating training and scaled training data
training_data = scaled_data[0:training_data_len, :]

x_train = []
y_train = []

for i in range(60,len(training_data)) :
    x_train.append(training_data[i-60:i,0])
    y_train.append(training_data[i,0])

#converting training data to numpy arrays

x_train,y_train = np.array(x_train),np.array(y_train)

#Reshaping our data
x_train = np.reshape(x_train, (x_train.shape[0],x_train.shape[1],1))
print(x_train.shape)

# Building our model

model= Sequential()
model.add(LSTM(50,return_sequences= True, input_shape=(x_train.shape[1],1)))
model.add(LSTM(50,return_sequences= False,))
model.add(Dense(25))
model.add(Dense(1))

# Compiling model
model.compile(optimizer='adam', loss='mean_squared_error')

# Training the model
model.fit(x_train,y_train,batch_size=1,epochs=100)

# Spliting into x and y test data sets
test_data= scaled_data[training_data_len-60:, :]
x_test=[]
y_test=dataset[training_data_len:, :]

for i in range(60, len(test_data)):
    x_test.append(test_data[i-60:i,0])

# Converting to numpy arrays
x_test = np.array(x_test)
x_test = np.reshape(x_test, (x_test.shape[0], x_test.shape[1], 1))

predictions= model.predict(x_test)
predictions= scaler.inverse_transform(predictions)

# Finding the mean squared error
rmse = np.sqrt(np.mean((predictions - y_test) ** 2))
print(rmse)
        

Intuitively this python model that I hastily constructed is seeking to predict historical S&P 500 prices by guessing tons of data points, all the while iteratively minimizing the difference between our guesses and actually predictions, using an algorithmic structure mimic neuronal activity. If we visualize the S&P 500 prices over time as follows:

What our algorithm is doing, mimicking quantum neural activity, is making thousands of guesses in and around our historical trend line, logically trying to reduce the distance between expected and actual outcomes (RSME). While my model didn't ultimately generate a forward prediction, it did compile, and I bet that if I can figure out how to adjust my parameters, it could potentially give me a startlingly accurate forward prediction. See below for what I mean. As my poor computer labored through the simulation, we could see that our loss, or RSME, was decreasing with each pass through the model:

So, what does this mean for me as an investor? Not much with the model as is. I disdain making shot-in-the dark guesses based on just numerical data alone, even if we are using smart numerical methods. Due to Murphy's Law, good ole cynicism, and my firm belief in skill-based alpha creation, I dislike the idea of generating trading ideas using ML as a retailer. These models are constrained by the quality and breadth of data we have available. Due to the asymmetry of market makers with deeper pockets, people more well connected within financial institutions who don't need to make quality guesses, or just people far more brilliant than you, in our brutal mixed economy, other people's machine learning models will cause you to lose out on trading success unless you get incredibly lucky. However, as an investor, neural networks and quantum thinking could be a silver bullet against the forces of the brutal mixed economy. The aspect of quantum thinking that could be groundbreaking to investors and traders, one that I have yet to mention, is the influence of consciousness. As a macro investor, I salivate at the prospect of being able to better model human thinking and action than we can now with our present flimsy bounded rationality functions and lagging macroeconomic indicators. Insofar as macroeconomic behavior is an emergent phenomenon resulting from the thoughts and actions of billions of people, past and present, we can use quantum thinking to apply our understanding of our society in a far more realistic manner than classical thinking. Imagine if we could pick apart the Fed's representative agent models and use pseudo-quantum equations, weighted by our best guess at the underlying wave function generated by a neuronal network that mimics quantum thinking, to dictate consumer preferences. We could elegantly combine the humanistic struggles and financial struggles people face in the competition for scarce resources, adding a layer for political struggles, a layer for competition for health equity, and a layer for discrimination, all enabled by the fact that our quantum thinking allows us to accept the pervasive reality that humans are artistic, fearful, numerical, creative, opportunity-maximizing, altruistic, and irrational all at once. In that quantum model, the limiting factor in being able to model that complex human reality will be our own inability to make interdisciplinary connections and our own ability to correctly create parameters that actually describe our reality instead of our false classical reality. Fortunately I feel well assured due to the splendors of my liberal arts education, for the rest of us, we might all want to open a book, read a philosophical treatise, or watch some C-SPAN(not patronizing you, just saying!)

Economics is due for a quantum revolution, driven by neural thinking and machine learning. We cannot yet model human consciousnesses mathematically; the question is still more theory than practice, yet I feel as though the revolution is inevitable. In the quantum world of the future, the investors who make money will be those who can both understand a return series and also figure out harmonize that mathematical thought with human emotion.