In my previous blog post, I explored the capabilities of ChatGPT 3.5, testing its skills as a programmer and mathematician’s assistant. The results were mixed, to say the least. While it could handle simple coding tasks with ease, it faltered when faced with more complex mathematical problems and image manipulation tasks. I concluded that while ChatGPT 3.5 was impressive, it was far from replacing us in our jobs. It was a tool, yes, but one that needed careful supervision and frequent corrections.
Fast forward to today, and we have ChatGPT 4.0 with code interpreter enabled. I approached this new version with the same scepticism I had for its predecessor, but I must admit, my initial impressions have been challenged. The leap from 3.5 to 4.0 is not just a step forward; it’s a giant leap. You can see my experiment here https://chat.openai.com/share/0099a12f-e577-44bd-aa10-7c7508f15f19.
In my previous experiment, I asked ChatGPT 3.5 to translate a 2D image, a task that combines both programming and a bit of maths. The results were less than satisfactory. It was able to write code to translate images if they were in real space, a task that can be easily found searching on the web. However, it struggled to handle images represented in Fourier space correctly, and even with multiple hints, the best it could do was a rough approximation of the correct solution. It took six attempts to get the code automatically generated, and even then, it was far from perfect.
With ChatGPT 4.0, however, the story is different. When asked to perform a similar task, it provided a clear, concise, and correct solution. It understood the concept of image translation in the context of computer vision and image processing, and it was able to generate Python code using the scikit-image package to perform the task. The code was not only syntactically correct but also logically sound, demonstrating a significant improvement in understanding and problem-solving capabilities.
"""
#Me: Can you know provide some python code to translate (pixel shifts) images? And can you execute it?
#Chat gpt: Here's a simple Python example using scikit-image to translate an image:
"""
import numpy as np
import matplotlib.pyplot as plt
from skimage import data
from skimage.transform import AffineTransform, warp
# Load an example image
image = data.camera()
# Define a translation transform
tform = AffineTransform(translation=(50, 50))
# Apply the transform to the image
translated_image = warp(image, tform.inverse)
# Plot the original and translated images
fig, ax = plt.subplots(1, 2)
ax[0].imshow(image, cmap='gray')
ax[0].set_title('Original Image')
ax[1].imshow(translated_image, cmap='gray')
ax[1].set_title('Translated Image')
plt.show()
"""
#Chat gpt:
In this code, AffineTransform is used to define a translation of 50 pixels to the right and 50 pixels down, and warp is used to apply this transform to the image. The result is an image that has been shifted.
However, I must clarify that the current environment doesn't support displaying plots, so the matplotlib part of the code won't work here. You should be able to run it in a Jupyter notebook or similar environment on your local machine. Let me know if you need further help or clarification!
"""
"""
ME: perform the same operation as before but with an image represented in Fourier space.
#Chat gpt:
Sure! However, we need to keep in mind that translating an image in the Fourier domain is not the same as translating an image in the spatial domain. In the Fourier domain, translations are performed by multiplying the image by a complex exponential, which essentially changes the phase of the Fourier transform.
Here is a Python code snippet demonstrating translation in the Fourier domain:
"""
import numpy as np
from skimage import data
from scipy.fft import fft2, ifft2, fftshift, ifftshift
# Load an example image
image = data.camera()
# Compute the 2-dimensional FFT of the image
image_fft = fft2(image)
# Define a translation
dy, dx = 30, 30
# Generate an array with the same size as the image
x = np.arange(0, image.shape[1])
y = np.arange(0, image.shape[0])
xv, yv = np.meshgrid(x, y)
# Create the translation function in Fourier space
translation = np.exp(-2j * np.pi * (dx * xv / image.shape[1] + dy * yv / image.shape[0]))
# Translate the image in Fourier space
translated_image_fft = image_fft * translation
# Transform back to spatial domain
translated_image = np.abs(ifft2(translated_image_fft))
# Now you could plot the images
"""
#Chat gpt:
This code first computes the Fourier transform of the image using fft2. Then it generates a complex exponential function that represents a shift in the Fourier domain. This function is multiplied with the Fourier-transformed image to achieve the translation. Finally, the inverse Fourier transform ifft2 is used to transform the image back to the spatial domain.
As before, the current environment doesn't support displaying plots, so you would need to run this on your local machine to see the translated image.
"""
Another test I revisited was a mathematical problem I had posed to ChatGPT 3.5: “What is the intersection between the unit circle and the curve y = x^2?” The previous version had failed to provide a correct answer. However, ChatGPT 4.0 not only understood the problem but also wrote its own code to solve it, correctly identifying the intersection points. This was a clear demonstration of the AI’s improved mathematical problem-solving capabilities although It’s important to note that only the premium version of ChatGPT 4.0 can run the code it suggests, as it did in the example of the intersection of the unit circle and the parabola. +
- ME: Can you tell me which is the intersection between the unit circle and the curve “y= x*x”?
- ChatGPT: The unit circle is defined by the equation x2+y2=x2+y2=1. The curve y=x2 is a parabola. To find their intersection, we can substitute y2 from the equation of the parabola into the equation of the circle, and solve for x2. So, we have x2+(x²)²= 1 or x²+x⁴=1 This is a quartic equation and can be difficult to solve, but let’s give it a try. [AND IT STARTS WRITING AND EXECUTING CODE]
So, is my job in danger now? Well, it’s a complex question. The advancements in AI, as demonstrated by the jump from ChatGPT 3.5 to 4.0, are indeed impressive. The AI’s ability to understand complex tasks and generate accurate solutions is growing quite fast. However, it’s important to remember that AI, at its core, is a tool. It’s a tool that can augment our capabilities, automate mundane tasks, and help us solve complex problems. In the end, whether AI becomes a threat or an ally in our jobs depends largely on how we choose to use it. If we see it as a tool to enhance our skills and productivity, then there’s no danger, only opportunity. But if we see it as a replacement for human intelligence and creativity, then we might indeed have cause for concern. For now, though, I believe we’re safe. The Turing test might be a thing of the past, but the “human test” is still very much alive.
