Facebook PixelCan dimensional analysis combined with brute computing power allow us to ‘manufacture’ new knowledge without any a priori understanding of ‘first principles’ and without recourse to empiricism?
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Can dimensional analysis combined with brute computing power allow us to ‘manufacture’ new knowledge without any a priori understanding of ‘first principles’ and without recourse to empiricism?

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Shireesh Apte
Shireesh Apte May 21, 2022
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Empirical science has racked up a vast body of heuristic relationships. Theorists find scientific and logical mechanisms associated with these relationships and attempt to derive them from; or trace them to; ‘first principles’. Either way, scientific reasoning has historically proceeded, and continues to proceed, a posteriori, i.e. using prior experience.
Good mathematical models describe and make temporal and spatial predictions about natural phenomena. Dimensional analysis dictates that an equation is true only if the units on the left hand side are equal to the units on the right hand side. Therefore, would it not be possible to take any number of physicochemical properties of matter and use iterative artificial intelligence (AI) algorithms to manipulate them until the units (on one side of the equation) matched those of the quantity that is being predicted (on the other side of the equation)? It may very well turn out that the physicochemical properties being manipulated (seemingly) have no relation to the prediction quantity; however, that may very well be one of the reasons to attempt such an exercise; viz. to find correlations between seemingly unrelated phenomena or physicochemical properties of matter that have not yet been explored empirically. In so doing, it may be necessary to assign physical significance to any dimensions that are left-over or do not match; so that the equation is made dimensionally true.
This approach becomes even more suited to prediction when AI is used to create a ‘training set’ for the algorithm. For example, a mere knowledge of whether or not two or more physicochemical properties are directly or inversely related allows the algorithm to significantly improve the equation output. The algorithm then searches through a list of properties to find one that satisfies the ‘left-over’ dimension units or has human intelligence take over to assign physical reality to leftover dimensional mathematical abstractions. There is no limit to the equations or predictors that can be subjected to this paradigm. It is projected to work as well in designing superior light harvesting or energy dense molecules and catalysts for fuel cells as it does with designing excipients that increase the solubility of APIs’ or decrease their biological off-target effects. It is surprising that no concerted scientific effort yet exists that uses this idea
dimensional analysiscreating knowledgemathematical equationsfirst principlesempiricala prioriartificial intelligencealgorithm
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Shubhankar Kulkarni
Shubhankar Kulkarni2 years ago
A complex but interesting idea!
Even if you could manufacture new knowledge, you would need to test it empirically to prove it, right? The way I see it, the machine or program will definitely give birth to new ideas but then the bottleneck would be at the level of identifying potentially useful knowledge out of the generated knowledge and pieces of knowledge that are empirically feasible. There are a lot of constraints that even the "training sets" will miss out on that come into play when you show something empirically. Therefore, not all knowledge might be "true" in a sense.
Also, in order for the knowledge generator program to be more useful, it should be a targeted program rather than a general one. It should generate knowledge with a problem in "mind" so it drives humans closer to the solution. What do you think?
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