3 ms·

I'm curious about HN readers so I made a poll: where you do see yourself in Tao's hierarchy? http://goo.gl/forms/KuXqj0wgZu http://goo.gl/forms/KuXqj0wgZu Edi

by j2kun 11y ago

I'm curious about HN readers so I made a poll: where you do see yourself in Tao's hierarchy? http://goo.gl/forms/KuXqj0wgZu http://goo.gl/forms/KuXqj0wgZu Edit: for those who are interested in the results, here's a one-click link https://docs.google.com/forms/d/1_RkOUYEoC4m9mYQZKexp2uSuj63wnq24QEGND6xBZ2M/viewanalytics?usp=form_confirm https://docs.google.com/forms/d/1_RkOUYEoC4m9mYQZKexp2uSuj63...

Tarrosion 11y ago
Can I choose all of the above? I'm finishing my second year of grad school, so I should be transitioning roughly from rigorous to post rigorous. Okay, that's probably true, but only in the areas of math I know best and use frequently. In other areas, I've never moved past the rigor stage; in yet others I'm not even that far along. I'm pretty comfortable with probability and optimization, which is my day-to-day. I will probably never be better at topology than I was when finishing my undergrad degree. And in my one brush with differential geometry, I struggled to reach the rigor. And even then it's more complicated, because human intuition is notoriously bad in probability.
- j2kun 11y ago
  I'd say pick the max over all subfields. I myself am about to get a PhD in mathematics yet I have an irrational fear of differential equations.
analog31 11y ago
Post rigorous, heading towards rigor mortis. ;-) This doesn't mean I'm a professional caliber mathematician -- I'm not, and a lot of my math education was in studying physics. It just represents which stages I've passed through, if those stages are valid It would be interesting to know if there are corresponding hierarchies in subjects such as science, computer programming, or even music.
- JadeNB 11y ago
  > It would be interesting to know if there are corresponding hierarchies in subjects such as science, computer programming, or even music. I think that you could probably apply the labels to just about any profession, or even hobby (I'm thinking of rock climbing as one close to my heart), and it might even be interesting, but it probably wouldn't have quite the same resonance: I don't think that there are many other fields where being rigorous is seen as an end in itself, and people already tend to think of post-rigorous proficiency in, say, music as a desireable state to reach.
- cossatot 11y ago
  My field is earth science which is, at its best, highly empirical. The stages are a little different: 1) Learning to observe and learning the basics of the theory; 2) Learning the theory quite a bit more and getting more practiced about observing with theory in mind; and 3) Hammering on, and molding or breaking, the theory with more observations or other theory. Unlike math, it's just really, really difficult to ascertain that the theory is correct and it's never correct at all levels. I have always called geology 'the science of exceptions' because many of our laws are actually tendencies, and given 4.6 billion years, any bug or loophole in the theory will be exploited--and this is when you really learn stuff. In practice, I actually think the three steps there are kind of fractally embedded throughout in the stages of one's career, one's individual research project, or the overarching evolution of the science. It's pretty fun.
Enzolangellotti 11y ago
Pre-rigorous, starting my journey.
- analog31 11y ago
  My only advice is: Enjoy it. Even if it's not your ultimate goal in life, I suggest treating it almost like a game. I don't know if programming is really like writing proofs, but there must be some similarities in terms of the emotional satisfaction that you get, for instance, when you find the missing piece that suddenly makes the whole thing work, or discover a weird twist that expresses your own personality.
- j2kun 11y ago
  Welcome to the club!
jzymbaluk 11y ago
I feel like I'm starting the transition from stage 1 into stage 2. I just completed calculus 3 and introduction to discrete mathematics (which I realize is still VERY early into math education), but I'm starting to be able to read proofs and be able to utilize concepts without needing to be able to strictly have any concrete applications for those concepts. It's very exciting, I feel like I'm finally able to play by the rules of math, and I'm looking forward to the places this newfound knowledge can take me.

by j2kun 11y ago

Tarrosion 11y ago

Can I choose all of the above? I'm finishing my second year of grad school, so I should be transitioning roughly from rigorous to post rigorous. Okay, that's probably true, but only in the areas of math I know best and use frequently. In other areas, I've never moved past the rigor stage; in yet others I'm not even that far along. I'm pretty comfortable with probability and optimization, which is my day-to-day. I will probably never be better at topology than I was when finishing my undergrad degree. And in my one brush with differential geometry, I struggled to reach the rigor. And even then it's more complicated, because human intuition is notoriously bad in probability.

j2kun 11y ago
I'd say pick the max over all subfields. I myself am about to get a PhD in mathematics yet I have an irrational fear of differential equations.

analog31 11y ago

Post rigorous, heading towards rigor mortis. ;-) This doesn't mean I'm a professional caliber mathematician -- I'm not, and a lot of my math education was in studying physics. It just represents which stages I've passed through, if those stages are valid It would be interesting to know if there are corresponding hierarchies in subjects such as science, computer programming, or even music.

JadeNB 11y ago
> It would be interesting to know if there are corresponding hierarchies in subjects such as science, computer programming, or even music. I think that you could probably apply the labels to just about any profession, or even hobby (I'm thinking of rock climbing as one close to my heart), and it might even be interesting, but it probably wouldn't have quite the same resonance: I don't think that there are many other fields where being rigorous is seen as an end in itself, and people already tend to think of post-rigorous proficiency in, say, music as a desireable state to reach.
cossatot 11y ago
My field is earth science which is, at its best, highly empirical. The stages are a little different: 1) Learning to observe and learning the basics of the theory; 2) Learning the theory quite a bit more and getting more practiced about observing with theory in mind; and 3) Hammering on, and molding or breaking, the theory with more observations or other theory. Unlike math, it's just really, really difficult to ascertain that the theory is correct and it's never correct at all levels. I have always called geology 'the science of exceptions' because many of our laws are actually tendencies, and given 4.6 billion years, any bug or loophole in the theory will be exploited--and this is when you really learn stuff. In practice, I actually think the three steps there are kind of fractally embedded throughout in the stages of one's career, one's individual research project, or the overarching evolution of the science. It's pretty fun.

Enzolangellotti 11y ago

Pre-rigorous, starting my journey.

analog31 11y ago
My only advice is: Enjoy it. Even if it's not your ultimate goal in life, I suggest treating it almost like a game. I don't know if programming is really like writing proofs, but there must be some similarities in terms of the emotional satisfaction that you get, for instance, when you find the missing piece that suddenly makes the whole thing work, or discover a weird twist that expresses your own personality.
j2kun 11y ago
Welcome to the club!

jzymbaluk 11y ago

I feel like I'm starting the transition from stage 1 into stage 2. I just completed calculus 3 and introduction to discrete mathematics (which I realize is still VERY early into math education), but I'm starting to be able to read proofs and be able to utilize concepts without needing to be able to strictly have any concrete applications for those concepts. It's very exciting, I feel like I'm finally able to play by the rules of math, and I'm looking forward to the places this newfound knowledge can take me.