A plea to make FOM the first priority in the education engineering curriculum of the 21st century

José Manuel Rodríguez Caballero josephcmac at gmail.com
Tue Mar 14 05:20:15 EDT 2023

Dear members of the FOM community,

Let us consider the case of a young child, named Socrates, who attempts to
solve a geometric problem and arrives at an incorrect result. Such an error
may have limited consequences, since those who lack the ability to
recognize their own mistakes are unlikely to convince society in technical
fields like natural science and engineering (I will avoid commenting
outside this domain).

Now, let us imagine Meno's robot, a powerful machine-learning tool,
attempting the same problem. With its vast database and processing power,
Meno's robot is likely to produce the correct solution. However, there is
still a risk of error that could be difficult to detect given the system's
training to persuade humans. If Meno's robot makes a fallacious argument,
it will be counterintuitive and could deceive even the most skilled
engineers. This is what mathematician Eric Weinstein calls OUTelligence
[6], in contrast to INtelligence.

An example of a counterintuitive fallacy that can deceive even engineers is
Simpson's paradox [4]. This paradox appears when a trend emerges in
different groups of data but disappears or reverses when these groups are
combined. If not analyzed correctly, the paradox can lead to incorrect
conclusions, since the trend in the overall data may not accurately reflect
the trends in individual groups.

For instance, concerns were raised about gender discrimination in graduate
admissions at the University of California, Berkeley in 1973. When the
admission data was analyzed, it appeared that men were admitted at a higher
rate than women in most departments. However, when the data was separated
by department, it was revealed [5] that women had a higher admission rate
than men in some departments. The paradox arose because women tended to
apply to more competitive departments, while men applied to less
competitive ones.

If the overall data had been used to make decisions, it could have led to
incorrect conclusions about gender bias in admissions. The Simpson's
paradox is a fallacy that can be counterintuitive and can deceive even
engineers if not analyzed carefully.

This analogy echoes Meno's paradox [3], which asks how we can seek
knowledge when we don't know what we are seeking. Education's priority
should be not just to generate solutions, but to verify them rigorously. We
are no longer living in the 20th century but in a time of myth comparable
to when humans coexisted with other intelligent non-human species like
Neanderthals. We must ensure that the level of rigor demonstrated by pure
mathematicians is transmitted to fields like engineering, which did not
require it in the past, to forestall future engineers' vulnerability to
AI-generated fallacies.

The fourth industrial revolution necessitates educational reforms that
cultivate intuition in the FOM field rather than memorization of algorithms
like fancy integral calculus methods that can be computed in seconds by
WolframAlpha [2]. Banning AI in schools [1] would be dangerous for
humanity, as it would expose future professionals to cosmic levels of
delusion emanating from electronic systems trained to be believable, which
is not necessarily the same as telling the truth.

Jose M. R. Caballero

[1] Don’t Ban ChatGPT in Schools. Teach With It.

[2] Conrad Wolfram : Enseigner les vraies mathématiques aux enfants avec

[3] Scott, Dominic. Plato's Meno. Cambridge University Press, 2006.

[4] Sprenger, Jan and Naftali Weinberger, "Simpson’s Paradox", The Stanford
Encyclopedia of Philosophy (Summer 2021 Edition), Edward N. Zalta (ed.),
URL = <https://plato.stanford.edu/archives/sum2021/entries/paradox-simpson/

[5] Bickel, Peter J., Eugene A. Hammel, and J. William O'Connell. "Sex Bias
in Graduate Admissions: Data from Berkeley: Measuring bias is harder than
is usually assumed, and the evidence is sometimes contrary to expectation."
Science 187.4175 (1975): 398-404.

[6] Eric Weinstein's The Portal Website, "Artificial Outelligence",
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