「ムーアの法則」は今後も成立するのかどうか？ JMPとChatGPTで考察してみた

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The recent ChatGPT (GPT-4) allows you to recognize images by uploading them.

So, I casually uploaded a JMP report like the one below in image format (png) to ChatGPT, and said, ``This is a report from fitting a curve in JMP. Please interpret the results.'' I tried the prompt.

It returned a document like this:

After this, I recognized the values of AICc, BIC, and R2 in this image and interpreted the results, but what surprised me most of all was the following sentence written at the end.

Wow, you recognize that this data shows "Moore's Law" even though you didn't specifically explain it! !

ChatGPT is scary.

"Moore's Law" and graphs showing it

Moore's Law is a law that states that the number of transistors installed in an integrated circuit doubles approximately every two years. Semiconductor technology is advancing day by day, and as the number of transistors installed increases, the processing power of devices increases significantly, and our daily lives benefit greatly from this.

The following graph is often used to explain Moore's Law.

The year is plotted on the horizontal axis (X), the logarithmically transformed number of transistors per microprocessor in that year is plotted on the vertical axis (Y), and a regression line is fitted. Here, we use a logarithm with a base of 2 to make it easier to understand that the value doubles in two years.

R-squared is very high at 0.994, and the regression line fits the data well. The regression equation shows that the number of log-transformed transistors increases by about 0.5 every year, so in two years it increases by about 1. If we return this to the original scale, the number of transistors roughly doubles every two years, which is Moore's Law itself.

Fit various nonlinear models with JMP's "Curve Fitting"

The previous section shows that the logarithmic transformation of the number of transistors (Y) follows a straight line, but when considered on the original scale, it shows that Y increases exponentially.

Therefore, the report shown at the beginning of this blog is the result of fitting a nonlinear model to the scale of Y without logarithmically transforming it.

Let's refer back to this report as we fit various nonlinear models using JMP's Curve Fitting platform.

Three models are fitted here: Logistic 3P (logistic model with 3 parameters), Weibull growth (growth curve), and Gompertz3P (Gompertz curve with 3 parameters).

When you look at the fitting line on the graph, it may appear that only one line is fitted, but all three models fit almost the same way, so they overlap.

In the "Model Comparison" report at the top of the report, you can compare the fit of each model using statistics such as AICc, BIC, and R-squared. As JMP specifications, the AICc is arranged from top to bottom in descending order of fit (better fit), so Logistic 3P is the best model, but the statistics of other models are similar, and the model It seems difficult to decide which is better or worse.

Will Moore's Law still hold true?

In the previous section, we fitted a nonlinear model using data from 1971 to 2021, but what would happen if we used these models to predict the future number of transistors?

In fact, predictions vary greatly depending on the model. The following shows the horizontal axis of the previous graph expanded to around 2040.

The orange Gomperz 3P model is a prediction that assumes that Moore's law will continue into the future. On the other hand, the Logistic 3P model and Weibull growth model are predictions that assume that Moore's law will break down midway through, and the growth in the number of transistors will slow down.

Indeed, in recent years, it has been said that Moore's Law has reached its limits. Then ask ChatGPT about the future of Moore's Law.

It seems certain that the limit has been reached to some extent. Physical and economic factors seem to be the key to maintaining Moore's Law in the future.

The fact that Moore's Law still applies today may be a result of the efforts of engineers to innovate in order to follow it. I look forward to technological innovations that will continue Moore's Law and make our lives better.

by Naohiro Masukawa (JMP Japan)

Naohiro Masukawa - JMP User Community

Data source: Our World in Data ( Moore's law: The number of transistors per microprocessor (ourworldindata.org) )