How urgent is it to intuitively understand Bayesianism?

The cur­rent state of my un­der­stand­ing (briefly):

  1. I very much un­der­stand re­duc­tion­ism and the dis­tinc­tion be­tween the map and the ter­ri­tory. And I very much un­der­stand that prob­a­bil­ity is in the mind.

  2. From what I un­der­stand, prior prob­a­bil­ity is just the prob­a­bil­ity you thought some­thing was go­ing to hap­pen be­fore hav­ing ob­served some ev­i­dence, and pos­te­rior prob­a­bil­ity is just the prob­a­bil­ity you think some­thing will hap­pen af­ter hav­ing ob­served that ev­i­dence.

  3. I don’t re­ally have a pre­cise way of us­ing ev­i­dence to up­date my be­liefs though. I’m try­ing to think of and ex­plain how I cur­rently use ev­i­dence to up­date my be­liefs, and I’m dis­ap­pointed to say that I am strug­gling. I guess I just sort of think some­thing along the lines of “I’d be un­likely that I ob­serve X if A were re­ally true. I ob­served X. I think it’s less likely that A is true now.”

  4. I’ve made at­tempts at learn­ing Bayes’ The­orm and stuff. When I think it through slowly, it makes sense. But it re­ally takes me time to think it through. Without refer­ring to ex­pla­na­tions and think­ing it through, I for­get it. And I know that that demon­strates my lack of “true” un­der­stand­ing. In gen­eral, my short term mem­ory and abil­ity to rea­son through quan­ti­ta­tive things quickly seems to be well above av­er­age, but far from elite. Prob­a­bly way be­low av­er­age amongst this com­mu­nity.

I definitely plan on tak­ing the time to study prob­a­bil­ity com­pletely and from the ground up. I also plan on do­ing this for math in gen­eral, and a hand­ful of other things as well.
  1. What are the prac­ti­cal benefits of hav­ing an in­tu­itive un­der­stand­ing of Bayes’ The­o­rem? If it helps, please name an ex­am­ple of how it im­pacted your day to­day.

  2. I men­tion in 3) that it takes me time to think it through. To those of you who con­sider your­selves to have an in­tu­itive un­der­stand­ing, do you have to think it through, or do you in­stinc­tively up­date in a Bayesian way?

  3. How ur­gent is it to in­tu­itively un­der­stand Bayesian think­ing? To use me as an ex­am­ple, my short-mid-term goals in­clude get­ting good at pro­gram­ming and start­ing a startup. I have a ways to go, and am work­ing to­wards these things. So I spend most of my time learn­ing pro­gram­ming right now. Is it worth me tak­ing a few weeks/​months to study prob­a­bil­ity?

I don’t in­tend for this post to just be about me. I sense that other’s have similar ques­tions, and that this post would be a use­ful refer­ence. So please keep this in mind and try to re­spond in such a way that would be use­ful to a wide au­di­ence. How­ever, I do think that con­crete ex­am­ples would be use­ful here, and so re­spond­ing to my par­tic­u­lar situ­a­tion would prob­a­bly be use­ful to that wide au­di­ence.