Intelligence - Artificial Intelligence (AI) versus Human Intelligence

AI, AI, AI! It's the "new thing out there," and we now see its incorporation into not only on the internet, in business, but - in increasing degrees - into education as well. As a math graduate, it is worthwhile to consider whether this tool is one to be embraced or regarded with concern. A simple experiment might shed light on the matter. Having recently done a cursory search on comparing heat pumps to the more traditional air conditioning units, the "all-knowing" AI provides the following analysis: "....A heat pump can achieve efficiencies of 300-400%, meaning it can produce three to four times more energy in heating than it consumes...." My goodness! We have defied the laws of physics! We have just created energy out of nothingness, violated Conservation of Energy. There is a term for this- "Magic!" This experiment would seem to indicate that extreme caution - at a minimum - is needed in incorporation of AI, unless we are willing to be risk be lead astray (as per the above experiment).. It seems that - at most - using AI sparingly to assist with tedious internet searches or self-tutoring or comparable tasks would be advisable. To make major decisions, including developing complex math modeling, it would seem to be highly advisable to ensure that human intelligence remain the primary tool utilized, with delegation of "mindless" or "near mindless" tasks to AI.

2025 SIAM Mega Math Challenge problem - staying cool as the world heats up

This year in particular - in light of recent ongoing national and international crises -my curiosity concerning SIAM's choice of challenge problem was particularly acute. (Our team at CAVA competed this year as well). Rather than finance-based math modeling as we have seen in the majority of recent years, this year's problem focused on engineering-based math applications, incorporating the effects of climate change and increasing incidence of life-threatening heat waves. Insofar as climate change is considered (as per the Bulletin of Atomic Scientists) our the 2nd greatest existential threat to our species, directing minds of our mathematically-inclinded gifted youth to addressing this threat would seem a very worthwhile endeavor. There are some points I might note by way of commentary. When asked to model temperature as a function of time, the model which - to my mind - seems most obvious and practical is that of a sinusoidal function, a particular instance of the wave function. As such, one need only obtain the parameters (A, B, C, D) of the equation y = A sin [B(x - C)] + D, or, equivalently, y = A cos [B(x - C)] + D, with value of C being the only significant difference between the two. A = the amplitude, or 1/2 (max - min), B = 2 PI / period (where period = 1 day, or 24 hours), C = horizontal shift relative to the beginning of the period, and D = midpoint for y (temperature), equal to max - min. That would seem to suffice for modeling outdoor temperature based on present data. Modeling of rising temperatures over the 20-year time as the challenge demanded (2025-2045) could be modeled using the relatively simple and pessimistic scenario of linear growth, or the more complicated scenario of logistic growth. Lastly, to model indoor temperature - given outdoor temperatures - it seems to my mind to be most practical to make use of prior studies in this area. (The competition rules allow finding other sources which are published and do not involve real-time interaction with humans, inclusive of posts). I notice - upon cursory search on the internet - a 2013 study by Nguyen, Schwartz, and Dockery which concluded that "At warmer outdoor temperatures, there is a strong correlation between indoor and outdoor temperature (Pearson correlation coefficient, r = 0.91, slope, β = 0.41), but at cooler temperatures, the association is weak (r = 0.40, β = 0.04). Results were similar for outdoor apparent temperature...." It seems to me that this is sufficient machinery to proceed with creating a viable mathematical model within a constricted time frame. Upon scrutinizing the winning entries' solutions, I notice that they all seem to have employed integration at a minimum. I might apologize for my naivety, but shall dare to pose the question "Why?" I would understand if one is using integration for the purpose of utilizing a logistic growth curve (optimistically) to incorporate gradual stabilization of climate change over the long-term. However, I noted use of integration coupled with Newton's law of cooling to model temperature change throughout the day. Yes, Newton's law of cooling, and the heat equation generally, do model heat transfer; however, is utilization of such truly needed? Also, many teams seem to have utilized Python, the current programming language of choice. (A few decades prior, C++ was the computer language of choice. This was replaced with Java. Now, it seems, Python is most prominent, and the above enunmerated languages are "medieval." Fortran is "ancient.") There is an analogy I might offer. Suppose you are in attendance at a dinner party as a required social or professional gathering. This dinner is being held at a formal restaurant, serving mostly meats which - owing to dietary restrictions or personal reservations - you are unable to eat. You must order something however, and have contented yourself with ordering a tempting dessert, a chocolate mousse cake with berries on the side. Being a formal restaurant, every place setting includes multiple utensils, including salad and dinner forks, teaspoon, tablespoon, regular knife, bread knife, and dinner knife. Which utensil(s) would you utilize to partake of your dessert? It seems to me that a fork - either fork - perhaps coupled with one of the spoons would suffice. Oh, but that steak knife is especially shiny, with an impressive serrated blade, and seems - in its creation - to display incredible engineering in its construction. You simply MUST use that steak knife! Not only that, but - oh, you have been practicing your fencing the past several months, and surely MUST impress your tablemates by displaying your fencing skills in some way. Perhaps if - while eating your mousse cake and berry salad with your shiny, beautifully engineered steak knife - you can figure out a way to display your fencing prowess at the same time. You proceed to literally attack your mousse cake. "En garde! Defend yourself, Mousse cake!" Hopefully your tablemates will refrain from fleeing in terror. Very well, you have displayed the entirety of your fencing training, but is that truly needed? I presume there will be some to many who will counter that my own suggested model is oversimplistic, and use of calculus and numerical programming are required. I do not dispute this; however, why reinvent the wheel unnecessarily? The study I cited above - which relates indoor to outdoor temperature - seems to have already incorporated this in determining this relationship. The late Isaac Newton himself - who was far from humble - conceded that his own developments in math and the sciences were built upon the achievements of former pioneers in the field. If the relationship is already established by PhD-level mathematicians, why not utilize the results of the research they have already done (especially within the context of a 14-hour competition)? It seems that one could model daily temperature data using a sinusoidal model, scaling the amplitude of the outside temperature by a factor of roughly 0.41 as per the above mentioned study and leaving the other parameters unchanged, and then adjust for the long-term projections of global warming to the extent that the above enumerated temperatures are impacted. The other factor which struck me as puzzling was the minimal emphasis which the top entries seem to have placed on energy efficiency, the advisability of modernizing air conditioning systems and transitioning to Zero Net Energy. I presume transitioning from traditional air conditioning to modern heat pumps, coupled with shifting to (eventually) all-renewable energy sources for electricity generation would largely alleviate the drain on the energy grid as per the challenge prompt. Also, encouraging or requiring homeowners and commercial building owners to install solar panels, preferably with backup generators to provide electricity in the event of power outages, would be beneficial as well. The last set of suggestions would seem to move somewhat off the path of traditional math modeling and enter into the realm of electrical engineering. Even so, it seems that some incorporation of these suggestions, along with "back of the envelope calculations" would improve the accuracy and usability of the model developed.