There are also dozens of constants involved that are possibly a better analog, very few of which end up memorized.
Biology is immeasurably harder than physics, the systems so much more complex and opaque and non amenable to fundamental explanation. Rote memorisation is a must.
Statements of this form are essentially always false: basically everything has the same difficulty because the standards for what constitutes progress in a field are set according to what the people working in it can do on average.
It's easy to write down what you thought of Infinite Jest, but in order to achieve any special success as a critic you're going to have to beat out everybody else that's doing the same thing. That makes it very hard. Likewise in an alternate universe where physics was easy, the standards for how much you had to say in a paper would rise until the average paper was about as substantial as it is now.
A successful critic isn't a critic, they're an author that writes for whoever is making them successful. So the critic at the top of academia would be the best at writing criticims that people understood: no garuntee of understanding the most, but that's still a skill that, say, Feynman would find it hard to replicate. The heirarchal nature of almost everything garuntees that there will always be "the best," and that they will be hard to beat, regardless of how much it means in the grand scheme of things. Finally, the scarcity of grant money means that participating in any field means beating the best: a regulatory effect that's at the center of the discussion.
For example, in physics they require p < 3e-7 for a discovery. While in biology it is p < 0.05 and sometimes even p < .1 is allowed.
If there is a lot of data they would have too many "discoveries" (it would seem too easy) so they need a more stringent threshold. If the data is very expensive they would have too few "discoveries" so the threshold gets relaxed.
Memorizing large numbers of facts give way to understanding and intuition in my experience. It’s quite similar to how a chess player’s experience regarding strategy starts out by exhaustively enumerating potential futures and eventually turns into an intuitive understanding of future plays and how training a neural network leads to a high dimensional manifold representation of a concept.
I will say that I'm skeptical of a lot of the work done in biology in relation to networks and complexity. It's often either done by those without sufficient mathematical background (and, typically, wholly statistically invalid) or a bunch of hand-wavy, feel-good nonsense for a sexy tagline by those who should know better.
Better work is done by researchers in complexity who analyze biological systems.
You have missed the point of my comment. Do you think Feynman lacked a vast amount of physics knowledge that he memorized (to use his phrasing)? Part of acquiring expertise in any area is the fact that you end up storing lots of information about that area so that you don’t need to look up every little detail or fact.
If you are going to have a serious discussion with biologists about cell processes you need to have lots of knowledge, names, etc. at the ready. Can't go looking up every little thing as you go along. It would be impossible communicate if you did that.
Feynman was being a jerk with that comment. His dismissiveness reminds me of comment that a well respected mathematician once made. “Quantumn mechanics is just such and such theory in dimesion 1.” Only ignorance allows one to hold such a belief.
Well, quantum mechanics is "just" 0+1 quantum field theory which is actually a good insight and not at all dismissive.
Is commutative algebra just a branch of set of theory? Are set theorists generally equipped to understand research papers on Galois Cohomology? No. Set theory is used in these areas but to suggest that these areas "are just aspects of set theory" is not all insightful.
This not at all the same. QM is a special case of QFT.
> To say that theoretical quantumn mechanics is just a small branch of mathematics is ignorance.
It’s not. That statement is objectively true.
> It is not insightful at all.
It is.
https://en.m.wikipedia.org/wiki/The_Unreasonable_Effectivene...
> Is commutative algebra just a branch of set of theory? Are set theorists generally equipped to understand research papers on Galois Cohomology? No. Set theory is used in these areas but to suggest that these areas "are just aspects of set theory" is not all insightful.
Intersection (overlap) is not the same as containment, so I have no idea why you’re bringing this up.
Sets are one way (among others) to encode such mathematical structures. This doesn’t mean these structures are sets. For example, is the empty set an element of pi? This question is meaningless because the answer would have to depend on the encoding being used, and not on the properties of pi itself. It’s imposing additional structure above and beyond that of the mathematical structure in question.
See here for more discussion: https://news.ycombinator.com/item?id=16080027.
No. It is a set together with additional structure. Without this additional structure you just have a set, not a ring.
> So is a group.
Again, no. It is a set together with additional structure.
Note: The collection of all groups is not even a set!