Question

Hello, Your Honor,
I was asked by a dear person:
Is there any article or information you know of on the subject of the halakhic measures used nowadays? What obligates me to measure Torah quantities with a meter stick and not the way our ancestors measured them—with the hand? What is wrong with checking according to the cubit of an average person, and so on?
 
Just recently I read Shnerb’s essay following your book, and the arguments there nicely broaden the question:

For thousands of years, Jews lived with the knowledge that the width of a sukkah is seven handbreadths, while a breach invalidates an eruv at ten cubits, and nobody asked what exactly the length of a cubit or a handbreadth was. The length measure of “a man’s cubit” was considered an exact thing: simply place the forearm of an adult who is neither a dwarf nor a giant, and you have the measure of a cubit. Every sensible person understood that there are small differences from one person to another, but apparently nobody was troubled by that. Likewise, the ruling of Rabbi Maharam Alshakar (Responsa of Maharam Alshakar, question 35), according to which a woman is permitted not to cover hair that extends outside her braid, was accepted simply enough without anyone bothering to ask what the maximum area of hair is.
And then Jews began demanding precision in measures and weights from their rabbis: how many centimeters is a cubit, what is the length of a handbreadth, and what is the volume of an egg. A person in our generation is incapable of accepting “an egg” as a definition of a measure when the local supermarket sells eggs sorted by volume.
The ultimate example, in my view, is fixing the measure of “the hand recoils from it.” As is known, the Talmud in tractate Sabbath (38a) rules that cooking involves heating food to the level at which the hand recoils from it. In this case, even in earlier times people noticed that there are different levels of sensitivity to heat, so they added the definition “such that a baby’s belly would be burned by it” — something like: water in which, if you wash your baby, its stomach would be burned. Today every religious child learns that the measure of “the hand recoils from it” is exactly 45 degrees Celsius… This too is something that borders on the ridiculous.
Our master, the Chafetz Chaim, in his book Mishnah Berurah, gives the measure of “the hand recoils from it” and “a baby’s belly would be burned by it” without hesitation, as though it were known to all; and a few decades later Jews need to measure a duck’s blood temperature in order to establish thresholds.
So quantification has taken over our Torah world, but so too have analytical thinking and dissection, in the form of getting down to “the root of the law” and investigations of “two laws,” “object and person,” spread through the greater part of the Torah world, mainly because of Rabbi Chaim of Brisk and his students…
Again, it seems we have no other choice but to think analytically. Rabbi Chaim already said that one who does not hold of “two laws” can bring to the seven blessings ashes from the burning of an idolatrous city, permitted for benefit because “a new entity has arrived here”…
In recent generations it was the Chazon Ish such that, when you read his teachings, you get the impression that he tried to “get into the head” of the tanna or amora, and not to analyze their words “from outside.” We, by contrast, are gradually losing that ability, and sometimes it seems to me that Torah students in our generation, more than they are students of Abaye and Rava, are students of Newton and Leibniz.

The direction that emerges from his words there, somehow following your book, is that quantification and analyticity have taken over the world, which affects the Torah world too. Is that indeed so? Can an Orthodox person accept such an explanation?
And perhaps we should explain that analyticity corrupted the simple intuition that lets you estimate an egg-bulk by eye?
[Someone answered the above that nowadays he also measures the tiles in his house with a tape measure, so it’s “allowed” to grant God that precision too… Sounds like a rather moralistic Lithuanian-style answer.]
Bottom line: what obligates us to stick to the updated measurements?
Thank you