Great stuff William! Love every second. It compliments my 5 decades of misunderstanding (frequentist) probability well. HAHA. Honestly, I had a solid year of graduate level probability theory and not once heard about any of this.
Lost me about 10 minutes in…I never had calculus and my last dalliance with probabilities was 20 years ago. Wish I had a better mind for this stuff.
I didn’t know about these lectures but they seem very interesting. I want to see the mystery animal! Is there a good place for adults in cognitive decline (I’m 50) to get back on the maths train? Who’s this Janes person you keep referring to?
I will! I like your lecture and style but I think overall I have a really hard time working with these types of functions. I really liked my CS algorithms class but ultimately couldn’t take anything away from it because it all just turned into a jumble of A’s, B’s, a’s, N’s, X’s, f’s, etc. I could never do proofs either. It’s very demoralizing.
I’m one of those people who has to constantly look back and remember what a thing was defined as. I takes me dozens of attempts to read a single chapter in a math book with very little retention. I understand abstraction and don’t have an issue with that…just can’t keep stuff straight before the lecture has left me in the dust. I figured there was some space between the imagined and the concrete where my mind slips a gear, owing, perhaps, to my right-brained-ness. There has to be a better way for not-quite-stupid-but-also-not-smart people, like me to learn this stuff.
I want to improve but also to have this knowledge to help my kid when she gets to advanced topics. Anyhow, I really appreciate the lecture!
The math is over my head, but I do consider infinity in the sense of eternal punishment (supposedly found in Scriptures). However, the Greek words aion, aionios, etc never had the sense of endlessness in normal usage. Aion is an "age" or "eon" (a timeframe with beginning and end), yet its adjective "aionios" is supposed to be without end. How can an adjective have greater meaning than the noun it is derived from?
So, "eternal" doesn't really mean forever in the Bible sense. Does infinity mean the same in this context?
I think you know more than I about this. But it does seem to mean, in this context, forever ontologically. I'll have more on this shortly, when we examine the idea of "frequentism".
B is the following:
M=red balls
N=total balls
K=number of draws before the K+1 draw
L=at least one red ball drawn in previous k draws
Rk+1=red ball on k+1 draw
P(no red balls in k draws)=(N-M choose K)/(N choose K)
=(N-M)(N-M-1)…(N-M-K+1)/N(N-1)…(N-K+1)
P(L|B)=1-P(no red balls drawn)=1 - (N-M)(N-M-1)…(N-M-K+1)/N(N-1)…(N-K+1)
Now Bayes gives P(Rk+1|BL)=P(BL|Rk+1)P(Rk+1)/P(BL)
We know P(BL)= from the above
but P(BL|Rk+1) = P(BL) if we know we draw a red ball on the k+1 and we don’t change the previous draws so we have
P(BL|Rk+1)=P(BL) then P(Rk+1|BL)=[P(BL)(M/N)]/P(BL)=M/N
Great stuff William! Love every second. It compliments my 5 decades of misunderstanding (frequentist) probability well. HAHA. Honestly, I had a solid year of graduate level probability theory and not once heard about any of this.
Lost me about 10 minutes in…I never had calculus and my last dalliance with probabilities was 20 years ago. Wish I had a better mind for this stuff.
I didn’t know about these lectures but they seem very interesting. I want to see the mystery animal! Is there a good place for adults in cognitive decline (I’m 50) to get back on the maths train? Who’s this Janes person you keep referring to?
Ah, ET Jaynes. Go back and watch/read some of the first lectures. No math!
I will! I like your lecture and style but I think overall I have a really hard time working with these types of functions. I really liked my CS algorithms class but ultimately couldn’t take anything away from it because it all just turned into a jumble of A’s, B’s, a’s, N’s, X’s, f’s, etc. I could never do proofs either. It’s very demoralizing.
I’m one of those people who has to constantly look back and remember what a thing was defined as. I takes me dozens of attempts to read a single chapter in a math book with very little retention. I understand abstraction and don’t have an issue with that…just can’t keep stuff straight before the lecture has left me in the dust. I figured there was some space between the imagined and the concrete where my mind slips a gear, owing, perhaps, to my right-brained-ness. There has to be a better way for not-quite-stupid-but-also-not-smart people, like me to learn this stuff.
I want to improve but also to have this knowledge to help my kid when she gets to advanced topics. Anyhow, I really appreciate the lecture!
The math is over my head, but I do consider infinity in the sense of eternal punishment (supposedly found in Scriptures). However, the Greek words aion, aionios, etc never had the sense of endlessness in normal usage. Aion is an "age" or "eon" (a timeframe with beginning and end), yet its adjective "aionios" is supposed to be without end. How can an adjective have greater meaning than the noun it is derived from?
So, "eternal" doesn't really mean forever in the Bible sense. Does infinity mean the same in this context?
I think you know more than I about this. But it does seem to mean, in this context, forever ontologically. I'll have more on this shortly, when we examine the idea of "frequentism".
This reminds me of a biography I read about George Cantor, set theory and the infinite. You may like it as well: https://www.amazon.com/Mystery-Aleph-Mathematics-Kabbalah-Infinity/dp/0743422996