# Randomness vs. Ignorance

A dis­tinc­tion I don’t see made of­ten enough is be­tween what I call ran­dom­ness and ig­no­rance. Roughly, ev­ery ex­pres­sion of un­cer­tainty is ei­ther about “where in the uni­verse am I?” or “what is the uni­verse like?” (or both). The former is the do­main of ran­dom­ness, the lat­ter of ig­no­rance.

Sup­pose you roll a die. You know that you’re in a situ­a­tion where you’ve just rol­led a die, and that, in roughly 1/​6th of the situ­a­tions where one has just rol­led a die, the die will come up a three. Thus, your un­cer­tainty about the die roll is ran­dom.

Sup­pose you’re won­der­ing whether or not an om­nipo­tent and im­mor­tal be­ing ex­ists. What­ever the an­swer is, it is the same ev­ery time some­one is ask­ing this ques­tion. Thus there is no ran­dom­ness in­volved, but you are ig­no­rant of what the an­swer is (though you might have a hunch).

Often, your un­cer­tainty will have com­po­nents of both. Sup­pose some­one hands you a die, you roll it five times, and ev­ery time you roll a three. You can prob­a­bly guess that the die is bi­ased. But why? One way to an­swer this ques­tion is that, in most of the situ­a­tions where one is handed a die and rolls it five times and gets the same num­ber five times, the die is bi­ased. You are ig­no­rant of ex­actly how of­ten this is the case, though. It could be the case ev­ery 9 out of 10 times this hap­pens, or per­haps ev­ery 8 out of 10 times. Now sup­pose you knew that it was 9 out of 10 times. Then it would still be ran­dom whether you are in one of the 9 cases, or in the tenth.

• It could be ar­gued that it’s all ig­no­rance. The die will roll the way that physics de­mands, based on the ve­loc­ity, roll, pitch, yaw of the die, and the sur­face prop­er­ties of the felt. There’s only one pos­si­ble out­come, you just don’t know it yet. If you roll a die in an opaque cup, the un­cer­tainty does not change in kind from the time you start shak­ing it to the time you slam it down—it’s all the same ig­no­rance un­til you ac­tu­ally look.

You can, if you like, be­lieve that there is un­knowa­bil­ity at the quan­tum level, but even that doesn’t im­ply true ran­dom­ness, just ig­no­rance of which branch you’ll find your per­cep­tive trail fol­low­ing.

Luck­ily (heh), Bayes’ The­o­rem doesn’t care. It works for up­dat­ing pre­dic­tions on ev­i­dence, re­gard­less of where un­cer­tainty comes from.

• It could be ar­gued that it’s all ig­no­rance. The die will roll the way that physics de­mands, based on the ve­loc­ity, roll, pitch, yaw of the die, and the sur­face prop­er­ties of the felt. There’s only one pos­si­ble out­come, you just don’t know it yet. If you roll a die in an opaque cup, the un­cer­tainty does not change in kind from the time you start shak­ing it to the time you slam it down—it’s all the same ig­no­rance un­til you ac­tu­ally look.
You can, if you like, be­lieve that there is un­knowa­bil­ity at the quan­tum level, but even that doesn’t im­ply true ran­dom­ness, just ig­no­rance of which branch you’ll find your per­cep­tive trail fol­low­ing.

I’m not go­ing to ar­gue for un­knowa­bil­ity at the quan­tum level, but I will ar­gue (in the next post) that you are not suffi­ciently smart to differ­en­ti­ate pre­cisely enough be­tween the differ­ent pos­si­ble situ­a­tions, and that’s why you have to group a bunch of differ­ent situ­a­tions to­gether, and that’s how you get what I call ran­dom­ness. I’m not ar­gu­ing for or against any kind of “true” ran­dom­ness. I agree that you can ar­gue it’s all ig­no­rance, but (I claim) not do­ing so will solve a lot of prob­lems

• It could be ar­gued that it’s all ig­no­rance. The die will roll the way that physics de­mands, based on the ve­loc­ity, roll, pitch, yaw of the die, and the sur­face prop­er­ties of the felt.

As­sum­ing physics is de­ter­minis­tic, which is not known to be the case.

You can, if you like, be­lieve that there is un­knowa­bil­ity at the quan­tum level, but even that doesn’t im­ply true ran­dom­ness, just ig­no­rance of which branch you’ll find your per­cep­tive trail following

As­sum­ing MWI is the cor­rect in­ter­pre­ta­tion of QM, which is also not known to he the case.

• This is aleatory (in­her­ent ran­dom­ness) vs. epistemic (knowl­edge) un­cer­tainty. You can parse this as un­cer­tainty in­her­ent in the pa­ram­e­ters vs. un­cer­tainty in­her­ent in your es­ti­mates of the pa­ram­e­ters /​ the pa­ram­e­ter­i­za­tion of the model.

This is a very im­por­tant dis­tinc­tion that has re­ceived treat­ment in the pre­dic­tion liter­a­ture but, in­deed, is not ap­plied enough to in­ter­pret­ing oth­ers’ pre­dic­tions among laypeo­ple.

• I’ve seen some aca­demic talk of this. Adam Bjorn­dahl at CMU has writ­ten some pa­pers where he re­frames situ­a­tions that nor­mally have ran­dom­ness as be­ing about the ig­no­rance of an agent. Not­ing that his pa­pers are very tech­ni­cal and I don’t know what if any good gen­eral in­sights there are to glean from them.