hi all. on vac this week & doing some new stuff (happy BTD US). there is a semifamous thousands-year old quote by sun-tzu maybe not yet contained in this blog (its been going thru my mind for quite awhile now, but wasnt able to find it in the blog via google). it is a quite favorite quote of business consultants which might tell you something about modern *“leave no prisoners”* business attitudes/ culture in our at-times militaristic/ hypercapitalistic modern age. (dramatic alpha-male stuff, but to put it more bluntly, one with a conscience/ empathy/ independent mind might wonder about the *“fine print,”* ie how many *“enemy…”* ** men **did sun-tzu kill personally or oversee killing as a general? …or even

**which includes**

*humans***? oh but ofc its utterly**

*women/ children**metaphorical*right?) 😮 😳

Strategy without tactics is the slowest route to victory. Tactics without strategy is the noise before defeat. –Sun Tzu.

collatz has been described as the very impenetrable/ unconquerable adversary. strategy/ tactics both play a key role and have commented at length on both. they are like a yin-yang combination. victory will likely not come without some kind of balance between the two.

have been more/ very tactical for quite awhile but have been musing on some overarching strategy/ perspective/ pov lately, thinking it all over at current point. this involves more abstraction.

couldnt find this basic idea pointed out in old blogs. was it? the key question is to prove *f(x) < g(x)* for all *x*. here *f(x)* is collatz stopping distance or some similar metric and *g(x)* is “any recursive function” (either time/ space bounded). now apparently *f(x)* in many related forms has extreme entropy, the “needle in haystack” property, and also “fat/ long tails” distribution, and fractal. earlier blogs have outlined the idea that it appears that victory seems to lie on the path of decreasing or minimizing entropy somehow. *g(x)* can be regarded as an orderly function from analytic mathematics and *f(x)* is “far from it” in the sense of being extremely disorderly.