5 ms·

Once upon a time, I worked in an area of mathematics called Algebraic Combinatorics, which dealt constantly with questions of 'how' and 'why.' The combinatoric

Once upon a time, I worked in an area of mathematics called Algebraic Combinatorics, which dealt constantly with questions of 'how' and 'why.' The combinatorics provided a 'how': Given a problem in algebra, we could make up some combinatorics that describe the system, and then prove some theorems that tell you precisely how to manipulate the system to get the answer you want. But this 'how' doesn't necessarily say much about 'why' such a solution must exist. On the other end, we had representation theory, which gave a sort of algebraic reason for the solution to exist, but would give you no help in how to actually construct the solution. It was extremely common for interesting problems to have difficulty on one side or the other. You've got a 'how' and spend dozens of grad-student-years (GSYs) trying to discover the 'why', or the reverse. Likewise, ML is giving us relatively cheap answers to the 'how' question. How do proteins fold? Well, now we have better answers. And those answers, carefully studied, should help with the 'why'. Now, instead of having just a start structure and an end structure, you /should/ be getting an explicit sequence of moves from the neural network. Studying /why/ some moves are better than others should yield progress on the overall why question. Along the way, getting answers to 'why' should help constrain the search space for AlphaFold, and allow it to come up with better answers faster. This basic question going forward is 'how do we distill crystallized knowledge from this black box algorithm?' It's going to be an important question in a range of sciences, basically anywhere that data >> knowledge. Finding answers won't be easy, but, hey, no one said good science has to be easy...

natalyarostova 7y ago
'Why' presupposes there is an answer that a human can understand. Why do self-driving cars work? Because there exists some function that maps raw inputs to outputs that correctly interact with reality. Why? Because the neural network fit the right curves.
- Koshkin 7y ago
  I think Feynman’s was the best answer to the “why” question: https://www.lesswrong.com/posts/W9rJv26sxs4g2B9bL/transcript-richard-feynman-on-why-questions https://www.lesswrong.com/posts/W9rJv26sxs4g2B9bL/transcript....
  - skybrian 7y ago
    I think that's different, first because the neural network has an indirect relationship with the physics, and second because Feynman was operating under a handicap: he was asked to give an explanation in terms the listener (who didn't know any physics) would understand. In the case of folding, when we ask "why" we might be asking why it folds one way and not the other. Causation has consequences, like for example we might want to know whether a small change to one part of the protein will significantly change how it folds. We might say some amino acids cause the fold and others don't. If you understand the mechanism behind something, you can control it better. Or, if you're interested in machine learning, you could ask what changes to the neural network make prediction better or worse and which parts of it matter the most, when it might make mistakes, and so on.
- ArnoVW 7y ago
  It is true, we will never know in the ultimate detail how each weight of each neuron must be placed and why. But that is simply because it is too intricate to understand everything. Just like we try to understand human behaviour not by understanding individual neurons, we reason on an abstract level, called psychology. To take your example building a SDC will teach us which aspects are the most complex, and which solutions work better than other for those aspects. Comparing those solutions will allow us to see what working solutions have in common, and give us theories that we can then test.
  - natalyarostova 7y ago
    That's a fair response, but I don't think it's universal. Or at least I should say it presupposes all complex phenomena have a parsimonious abstraction layer a human brain can grok. Which, to be fair, does seem to hold true a surprising amount of the time. But I don't think it's required.
- commandlinefan 7y ago
  Well, you’re still not going to get to hand-wave away the “why” question. I’ve been working on recommender systems for the past 5 or so years, and I end up spending a lot of my time trying to work backwards to explain why the recommender recommended something that seemed counterintuitive (sometimes because of a bug, sometimes because of the model, sometimes for reasonable reasons). If you work on self driving cars, you’ll similarly be researching and explaining “why” this one drove into a lake this one time.
  - natalyarostova 7y ago
    Yeah that's a reasonable counter point to my example, you're right. I guess I used a poor example to try and make a more general point that there will and may already be a time when the black boxes we use exceed our ability to understand the causal mechanisms.
- jacquesm 7y ago
  > Why do self-driving cars work? Unless there has been some breakthrough that I'm not aware of this isn't true.
  - MaulingMonkey 7y ago
    They've worked conditionally for a long time now. It's not level 5 open world "works in all conditions" self-driving - but neither is it level 0 no automation whatsoever. Nor can humans drive unconditionally either.
    - jacquesm 7y ago
      A three year old can 'conditionally' drive a car. That doesn't mean it works.
reaperducer 7y ago
Reminds me of something I've heard often about history. That it's not enough to know that things happened. It's equally important to know why things happened. I apply this to a lot of fields, and it brings a better level of understanding. For example, knowing that storing text in MySQL as utf8mb4 is better than storing it as utf8 will get you a job. But knowing why storing text as utf8mb4 is better than utf8 will build you a career.
- tasogare 7y ago
  You cannot compare something like understanding history with an implementation detail of a DBMS, moreover an easy one like handling BMP or the whole standard Unicode (MySQL made a mistake here of calling utf8 something that doesn’t handle characters outside BMP).
  - erikpukinskis 7y ago
    There’s very little you can’t compare. Douglas Hofstadter (and others) made the argument that analogy is the foundation of cognition. Our brains are capable to tying together almost any two concepts. We sometimes teach ourselves to avoid certain connections, but the capability is there. Physics-wise, there will be some degree of resonance between any two circuits that aren’t an exact mirror of each other. And mirror circuits can be compared most easily of all.
  - reaperducer 7y ago
    You cannot compare something like understanding history with an implementation detail of a DBMS Sure, I can. I just did. Look at the comment you replied to. It does exactly that.

natalyarostova 7y ago

'Why' presupposes there is an answer that a human can understand. Why do self-driving cars work? Because there exists some function that maps raw inputs to outputs that correctly interact with reality. Why? Because the neural network fit the right curves.

Koshkin 7y ago
I think Feynman’s was the best answer to the “why” question: https://www.lesswrong.com/posts/W9rJv26sxs4g2B9bL/transcript-richard-feynman-on-why-questions https://www.lesswrong.com/posts/W9rJv26sxs4g2B9bL/transcript....
- skybrian 7y ago
  I think that's different, first because the neural network has an indirect relationship with the physics, and second because Feynman was operating under a handicap: he was asked to give an explanation in terms the listener (who didn't know any physics) would understand. In the case of folding, when we ask "why" we might be asking why it folds one way and not the other. Causation has consequences, like for example we might want to know whether a small change to one part of the protein will significantly change how it folds. We might say some amino acids cause the fold and others don't. If you understand the mechanism behind something, you can control it better. Or, if you're interested in machine learning, you could ask what changes to the neural network make prediction better or worse and which parts of it matter the most, when it might make mistakes, and so on.
ArnoVW 7y ago
It is true, we will never know in the ultimate detail how each weight of each neuron must be placed and why. But that is simply because it is too intricate to understand everything. Just like we try to understand human behaviour not by understanding individual neurons, we reason on an abstract level, called psychology. To take your example building a SDC will teach us which aspects are the most complex, and which solutions work better than other for those aspects. Comparing those solutions will allow us to see what working solutions have in common, and give us theories that we can then test.
- natalyarostova 7y ago
  That's a fair response, but I don't think it's universal. Or at least I should say it presupposes all complex phenomena have a parsimonious abstraction layer a human brain can grok. Which, to be fair, does seem to hold true a surprising amount of the time. But I don't think it's required.
commandlinefan 7y ago
Well, you’re still not going to get to hand-wave away the “why” question. I’ve been working on recommender systems for the past 5 or so years, and I end up spending a lot of my time trying to work backwards to explain why the recommender recommended something that seemed counterintuitive (sometimes because of a bug, sometimes because of the model, sometimes for reasonable reasons). If you work on self driving cars, you’ll similarly be researching and explaining “why” this one drove into a lake this one time.
- natalyarostova 7y ago
  Yeah that's a reasonable counter point to my example, you're right. I guess I used a poor example to try and make a more general point that there will and may already be a time when the black boxes we use exceed our ability to understand the causal mechanisms.
jacquesm 7y ago
> Why do self-driving cars work? Unless there has been some breakthrough that I'm not aware of this isn't true.
- MaulingMonkey 7y ago
  They've worked conditionally for a long time now. It's not level 5 open world "works in all conditions" self-driving - but neither is it level 0 no automation whatsoever. Nor can humans drive unconditionally either.
  - jacquesm 7y ago
    A three year old can 'conditionally' drive a car. That doesn't mean it works.

reaperducer 7y ago

Reminds me of something I've heard often about history. That it's not enough to know that things happened. It's equally important to know why things happened. I apply this to a lot of fields, and it brings a better level of understanding. For example, knowing that storing text in MySQL as utf8mb4 is better than storing it as utf8 will get you a job. But knowing why storing text as utf8mb4 is better than utf8 will build you a career.

tasogare 7y ago
You cannot compare something like understanding history with an implementation detail of a DBMS, moreover an easy one like handling BMP or the whole standard Unicode (MySQL made a mistake here of calling utf8 something that doesn’t handle characters outside BMP).
- erikpukinskis 7y ago
  There’s very little you can’t compare. Douglas Hofstadter (and others) made the argument that analogy is the foundation of cognition. Our brains are capable to tying together almost any two concepts. We sometimes teach ourselves to avoid certain connections, but the capability is there. Physics-wise, there will be some degree of resonance between any two circuits that aren’t an exact mirror of each other. And mirror circuits can be compared most easily of all.
- reaperducer 7y ago
  You cannot compare something like understanding history with an implementation detail of a DBMS Sure, I can. I just did. Look at the comment you replied to. It does exactly that.