And Abraham drew near, and said: ‘Wilt Thou indeed sweep away the righteous with the wicked? Perhaps there are fifty righteous within the city; wilt Thou indeed sweep away and not forgive the place for the fifty righteous that are therein? That be far from Thee to do after this manner, to slay the righteous with the wicked, that so the righteous should be as the wicked; that be far from Thee; shall not the Judge of all the earth do justly?’ And the Lord said: ‘If I find in Sodom fifty righteous within the city, then I will forgive all the place for their sake.’ And Abraham answered and said: ‘Behold now, I have taken upon me to speak unto the Lord, who am but dust and ashes. Perhaps there shall lack five of the fifty righteous; wilt Thou destroy all the city for lack of five?’ And He said: ‘I will not destroy it, if I find there forty and five.’ And he spoke unto Him yet again, and said: ‘Perhaps there shall be forty found there.’ And He said: ‘I will not do it for the forty’s sake.’ And he said: ‘Oh, let not the Lord be angry, and I will speak. Perhaps there shall thirty be found there.’ And He said: ‘I will not do it, if I find thirty there.’ And he said: ‘Behold now, I have taken upon me to speak unto the Lord. Perhaps there shall be twenty found there.’ And He said: ‘I will not destroy it for the twenty’s sake.’
Every year I read these verses in the Torah portion of Vayera and wonder about Abrahams’s negotiation strategy—what a puzzling sequence of numbers—50, 5, 45, 40, 30, 20, 10! There does not appear to be any discernible mathematical pattern here. Until I realized that Avraham was stress-testing the judgment.
Hearing that the Almighty decided to punish the cities of Sodom valley, Abraham decided to negotiate forgiveness for the people if a certain number of righteous people were to be found among them. But how many?
Abraham starts by throwing the number 50, which seems large enough to elicit forgiveness and small enough to be realistic. Having obtained G‑d’s acquiescence to this number, Abraham does what any good scientist or engineer would do—he stress-tests that number. He takes 10% of the original number—5 (10% of 50 is 5) and subjects his initial number to a stress-test: “Perhaps there shall lack five of the fifty righteous; wilt Thou destroy all the city for lack of five?” The number withstood the stress-test as G‑d agreed not to punish Sodom even if there were 45 righteous people in it.
That emboldens Abraham to subject the initial number to bigger stress—20% (20% of 50 is 10), so he asked if G‑d would not forgive Sodom if there were 40 (50 – 10) people there. Again, having obtained G‑d’s agreement, Abraham decides to further stress-test the initial number by applying progressively greater stress—40% (giving the number 50-20=30), 60% (giving the number 50-30=20), and 80% (giving the number 50-40=10). In each of these iterations of stress-testing, Abraham increases the “stress” by 20%—one-fifth of his original number.
This simple technique of stress-testing the initial assumption accounts for all the numbers in this dialog.
We further notice that the common denominator of this number sequence—50, 5, 45, 40, 30, 20, 10—is 5. This is a clear reference to five chasodim—five attributes of kindness (chesed or pl. chasodim) that Abraham personified. This interpretation may explain why Abraham started with the number fifty. In Kabbalah, every sefirah (Divine emanation) includes all ten sefirot in a fractal tree-like structure. Generally, every concept that can be expressed as a number reaches its full development when multiplied by ten (because of the interinclusion of all sefirot in each sefirah, as mentioned above). Starting with five attributes of kindness, Abraham may have thought that the number fifty is the maximum number related to kindness. Therefore he started by saying, “Perhaps there are fifty righteous within the city…” That may be why he started with fifty. This may also explain why Abraham used the number five as his initial stress-test saying, “Perhaps there shall lack five…” It may also explain why Abraham stopped after the five rounds of negotiations (or iterations of stress-testing) as he drew upon each of the five attributes of kindness he personified.