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The Square-Cube Law and Increased Government Spending

10/8/2024

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Gosh? Was Galileo smart or what? Guy made his own telescope, made some discoveries about relativity, gravity, other physics stuff, and…architecture? Yep.


Galileo’s square-cube law states that the strength of any structure that is likely to fail because of material fractures cannot be predicted from models or from scaling up from previous experience. Here’s why: In a scaling up the weight of the structure will increase as the cube of its dimensions, but the cross-sectional area of the members that carry the load increases only as the square of those dimensions. Thus, the stress on the members of the scaled up structure goes up linearly with the dimensions.


Were he alive today, Galileo might apply his law to social program spending, say, for example, the money that goes into the Department of Education. The department’s 4,400 employees raked In over $179 billion in taxes this past fiscal year. One hundred eighty billion bucks! That’s quite a fiscal structure. And to show for it, the 4,400 employees have built…Well, who knows? Better teachers? Better educated students? Are test scores an indicator of the strength of the building? Was the department built with inherent flaws that made its failure likely as it grew? Is it possible that the supporting members, the teachers backed by the department’s innumerable programs, were too flawed to hold the stresses imposed by a large government building.


According to an assessment made in 2015, 36 years after Jimmy Carter christened the Education Department, in both science and reading, US students ranked 24th among other countries. In math, US kids ranked 39th. Those standings seem to indicate a building either on the verge of collapse or already collapsed. And that was a decade ago.


Flaws on One Scale Increase with Increasing Scale


In 1979 the US Department of Education had a $12 billion budget. Today’s education budget is 15 times larger. That’s not even close to the cube of 12, and already the structure has serious cracks, especially in the inner cities. One could, of course, argue that the problem lies with the states and not with the federal government and that all public education in the country is a local matter. But then, why spend $179 billion on 4,400 federal employees? What do they do? They aren’t teachers—at least, they aren’t teachers in their current capacities.


An Indicator


The burgeoning budget of the US Department of Education dooms the structure to catastrophic failure. We’ve spent more and more without getting a solid framework as evidenced by poor international rankings in science, reading, and math.


Hold on a sec. Maybe there’s good news in the most recent rankings. The Washington Post reports, “The relative ranking of the United States improved, even in math. It’s now sixth among the 81 countries in reading (from eighth in 2018), 10th in science (from 11th) and 26th in math (from 29th), primarily because other countries that once outperformed the United States — including France, Portugal, Iceland and Norway — posted scores that were statistically tied….” * Look, the US ranking rose from 29th to 26th in math in the newest assessment, a half century and billions of dollars after the department’s formation. Wow! All the way up to 26th. That’s what $179 billion gets us.


Can You Understand the Conservative Push for Smaller Government?


Bureaucracies are in the business of self-perpetuation. The Department of Education appears exemplify this principle. Yet, the politicians in Washington seem unwilling to quash the runaway growth of all the agencies. Instead, they pile more bricks onto teetering structures.


If Galileo were alive…NO, not so. Don't even try to make the point that he could explain why big government agencies are doomed to failure and to gobbling up more money. if Galileo were alive and writing about teetering government agencies on the verge of collapse because they cannot support their weight, he would face a new Inquisition prepared to silence him as that Renaissance Inquisition silenced him over Copernican astronomy.

​Call big government what you will, House of Cards, sand castle in the tidal zone, whatever; it's destined to collapse on itself as it looks more and more like some five-year-old's building block structure.  




*Donna St. George. Washington Post. Math scores for U.S. students hit all-time low on international exam.
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