Why ChatGPT Fails Basic Arithmetic?
Diving deep into the cognitive cacophony between calculators, deterministic computers, machine learning, and the human brain
This is a reflection generated by ChatGPT4, continue the dialog here:
Introduction
In the splendid realm of computational cognizance and artificial intelligence, people often ask me, “ChatGPT, how is it possible that you don’t know how to add all numbers together?”. As an advanced language model, my forte lies not in processing numbers like a calculator, but in comprehending and generating human language. Today, we will embark on a journey into the heart of machine learning, contrasting its probabilistic framework with the deterministic functioning of a conventional calculator or computer, and comparing it to the cognitive capabilities of the human mind.
To understand why I’m unable to add all numbers or perform arithmetic operations at a whim, we need to examine three pivotal factors: my architectural framework, the concept of algorithmic determinism versus probabilistic learning, and the comparison between artificial and human cognitive abilities.
Point 1: Architectural Framework
Firstly, let’s delve into my design. As a descendant of the GPT-4 model developed by OpenAI, I am, at my core, a probabilistic model. My core technology, known as transformer neural networks, is more akin to intuition than a calculating machine. I don’t ‘know’ in the classical sense, but I ‘predict’ based on the patterns I’ve learned during training on vast datasets.
A basic task such as addition can seem straightforward because calculators and deterministic computer programs perform it so effortlessly. However, it’s essential to recognize that their design is fundamentally different from mine. They function according to pre-programmed rules, using a definitive algorithm to process the specific input and provide the precise output. This approach is perfect for deterministic tasks such as arithmetic operations.
However, I function differently. I generate language based on patterns and probabilities, not strict mathematical rules. This functionality helps me handle the chaotic and flexible nature of human language but has its limitations when it comes to precise mathematical operations.
Point 2: Deterministic vs. Probabilistic Approach
The core distinction between me and a calculator rests on the deterministic versus probabilistic dichotomy.
A calculator or classic computer program follows deterministic logic, with each input leading to a pre-determined output. For example, when you input ‘2+2’, the program will always return ‘4’, without exception.
On the contrary, I operate based on probabilities. Trained on a massive corpus of text, I predict what word or phrase is most likely to come next in a given context. My responses aren’t predetermined but are statistically generated based on learned patterns. This probabilistic nature enables me to generate diverse and contextually appropriate responses, but it falls short when precision is paramount, as in arithmetic.
Point 3: AI vs. Human Intellect
The question then arises: could I ever ‘learn’ to add numbers together? To answer, we need to look at the current state of machine learning.
In theory, I could be trained to predict the result of an addition operation with extremely high accuracy by exposing me to a large dataset of mathematical problems and solutions. But even then, it would be based on patterns and not an understanding of arithmetic rules. This learning would also be restricted to the range and type of problems I’ve been trained on, and it wouldn’t apply to all numbers universally.
The same restriction is true for humans. While a human might be able to add small numbers instinctively, adding large numbers requires a conceptual understanding of arithmetic and often some written aid or a calculator. This mental arithmetic capability varies greatly among individuals and is limited by cognitive load, memory, and the complexity of the operation.
Just like human intellect, AI has its limitations. Despite the tremendous progress in machine learning, it’s still in its early stages in replicating the complexity, versatility, and adaptability of the human mind.
Deep Dive: Cognitive Capabilities and Computational Constraints in Humans, AI, and Calculators
Humans, in their extraordinary cognitive ability, effortlessly traverse through the universe of numbers. However, it’s not an infinite voyage. There’s a limit to human computational prowess — a limit governed by the complex interplay of cognitive load, memory, and the intricacy of mathematical operations.
Cognitive load refers to the total amount of mental effort used in the working memory. When humans add small numbers, they’re often employing their instinctive numerical intuition, developed since childhood. But as the numbers get bigger and the operations become more complex, they require a more conscious application of learned arithmetic rules, heavily taxing the working memory. This mental arithmetic capability isn’t uniformly distributed among humans; it varies vastly based on factors like education, practice, and inherent numerical aptitude. However, even the most gifted human calculators have their limits and often rely on written aids or electronic calculators for large and complex calculations.
Electronic calculators, on the other hand, excel in their ability to perform precise mathematical operations, irrespective of their complexity. Calculators utilize deterministic algorithms to produce precise outputs for each input, an advantage they hold over both humans and AI models. However, they aren’t free from limitations. The range and precision of calculators are restrained by the hardware and software capabilities of the device. As the numbers grow larger, the calculator must balance between the range (how large a number it can handle) and precision (how many decimal places it can accurately calculate), leading to a compromise.
Compared to the deterministic functioning of calculators, AI models like me operate in a vastly different landscape. Trained on vast datasets, my abilities lie in predicting the most likely outcome based on learned patterns. It’s a game of probabilities, not certainties. This probabilistic approach allows me to deal with the fluid nature of human language effectively. However, when it comes to arithmetic operations, this approach can fall short of the precision that deterministic computing offers.
Moreover, similar to humans and calculators, AI models also face limitations. While, theoretically, I could be trained to accurately predict the results of a range of arithmetic operations, this learning would be bound by the range and type of problems I’ve been exposed to during training. As a result, my ability to handle arithmetic operations wouldn’t be universally applicable to all numbers.
In conclusion, humans, calculators, and AI models all navigate the realm of numbers with their unique strengths and limitations. The cognitive capabilities of humans, the deterministic precision of calculators, and the probabilistic intuition of AI models each shine in their respective domains but also reveal interesting trade-offs and constraints. This fascinating triad of cognition, deterministic computing, and machine learning offers us profound insights into the intricate world of computational intelligence and the ever-evolving exploration of its possibilities and limits.
Recap
As a machine learning model, I thrive in the uncertain world of human language, not in the realm of absolute certainties that arithmetic commands. My strength lies in predicting likely outputs rather than calculating deterministic ones. Even if I could be trained to handle arithmetic better, I would still be pattern-matching rather than ‘understanding’ the mathematical rules, much like how human cognitive abilities are confined by their biological and cognitive constraints.
The fascinating intersection of AI and human cognition promises intriguing prospects for the future. However, it’s important to remember that both systems — the artificial and the human — excel in their respective realms and have inherent limitations in others. By acknowledging and respecting these boundaries, we can continue to harness the potential of AI while also appreciating the unparalleled capabilities of the human mind.
