I like the way you talk straight about it. That's actually quite rare. Something that struck me about your notebook is it contained all numbers and graphs. But you said about transferable skills you know differential equations and linear algebra. How much do you actually do of that rather than use what you learned to make a computer do it? Like, do you actually get a better innate knowledge of those techniques or you get better at driving the computer and sense checking its output?
Thanks! The most important skill by far is the use of deductive reasoning, and although you could say I did not need all that math and physics for that, I think working our logic engine on several math subfields helps. I meant that if you know enough math, you can understand many technical fields better than someone without a technical background. Another great skill, and it can come out of many fields, is the analysis of large data sets with many variables. I did not mention that aspect, and the notebook does not by itself tell that story.
@mathematicaladventures I see, thanks for that. I studied theoretical physics but I had to cut and run for industry before PhD for fairly tragic personal reasons. Went into cyber security. I made heavy use of mathematical intuition (stability/variable relationships, graph theory principles/results etc.) but little if anything of "real" application of maths (until recently, but that's special). I was also wondering if the PhD made a lot of space for doing a lot of maths "properly" (by hand, so the Brain really learns intuition), or really was just pressured to throw things at the CAS and get results.
I also had a family tragedy during my PhD..... life happens. There is no shame in not finishing. I am glad you ended up in what has to be one of the most stable jobs around thanks to so much ill-intentioned hacking. As for math by hand, which I do a lot of in this hobby period, none was to be had during my research. It was all hard-core analysis of data, and so much of it, that I could talk about it for hours!
@mathematicaladventures I didn't even get to start let alone drop out! Interesting that your actual maths is more of a hobby and the PhD more number crunchy. I never left maths, although I put it on the shelf for sometime as I thought Sympy was better than I'll ever be and I was always a wizz with coding. Over the last few years particularly I've been buying up very old textbooks (some older than the USA) and working through all of mathematics from first principles; Greek geometry > Arab spherical/projective > Early European > Post-Hilbert > String theory. It's been a wild ride. There seems to be a fundamental disconnect between what mathematics and physics were before and after Hilbert. I think this, taken to extremes, is why string theory is nuts and practical high energy physics is about numerical approximations. Recall that Feynmann's great insight was "let's integrate this divergent series"; had anyone else said that, they'd be laughed out of academia entirely. I'm pretty sure we have to peel all the way back to Euler and walk back forward along a different path to fix the mess. Fortunately; Hamilton, Maxwell, and Tait already went far along such a path... although it is overgrown, it can still be made out. I've gone down it, and it does lead to a whole different world. However, that whole different world has its own traps. I'm working on a book and/or video series on it. How can I contact you to share a draft when it's ready?
I have wanted to do something like what you are doing, but that will definitely have to wait for retirement. It takes a lot more time to go back to the classics and go down those paths. The Number Theory book by Gauss is a case in point. I would love to work through it, but those are some difficult pages. I need a full time effort for something like that. This channel needs an email, let me go get one and I will post it here as well as more broadly.
May you please describe what you mean by “analysis”, I hear it used a lot but have yet to find a nice definition. I will go look, but I hope you can answer my question.
So Analysis can mean to analyze data as I did during my graduate work, but in mathematics (and I thankfully have gotten to read and learn a lot of analysis) Analysis is Mathematical Analysis, which is really "Calculus but with everything proven" or "All the proofs that show us that Calculus works." Here is the Wikipedia article: www.wikiwand.com/en/articles/Mathematical_analysis Mathematical Analysis has many branches (Real, Complex, Functional, Fourier, Harmonic,...) Does that help?
i'm totally down to listen to a rant about string theory
cool!
Me too
I have my outline ready, just need to find the time to make the video.
Congratulations on your academic achievement
Thanks! I still have a lot I would like to learn! I hope you too are interested in some of this learning.
I’m not as educated in your topics as you are. It doesn’t stop imagination. Some smart persons like you are apparently will act on it.
That's right, not knowing a topic is not a hindrance to the imagination!
I like the way you talk straight about it. That's actually quite rare.
Something that struck me about your notebook is it contained all numbers and graphs. But you said about transferable skills you know differential equations and linear algebra. How much do you actually do of that rather than use what you learned to make a computer do it? Like, do you actually get a better innate knowledge of those techniques or you get better at driving the computer and sense checking its output?
Thanks! The most important skill by far is the use of deductive reasoning, and although you could say I did not need all that math and physics for that, I think working our logic engine on several math subfields helps. I meant that if you know enough math, you can understand many technical fields better than someone without a technical background.
Another great skill, and it can come out of many fields, is the analysis of large data sets with many variables. I did not mention that aspect, and the notebook does not by itself tell that story.
@mathematicaladventures I see, thanks for that. I studied theoretical physics but I had to cut and run for industry before PhD for fairly tragic personal reasons. Went into cyber security.
I made heavy use of mathematical intuition (stability/variable relationships, graph theory principles/results etc.) but little if anything of "real" application of maths (until recently, but that's special).
I was also wondering if the PhD made a lot of space for doing a lot of maths "properly" (by hand, so the Brain really learns intuition), or really was just pressured to throw things at the CAS and get results.
I also had a family tragedy during my PhD..... life happens. There is no shame in not finishing. I am glad you ended up in what has to be one of the most stable jobs around thanks to so much ill-intentioned hacking.
As for math by hand, which I do a lot of in this hobby period, none was to be had during my research. It was all hard-core analysis of data, and so much of it, that I could talk about it for hours!
@mathematicaladventures I didn't even get to start let alone drop out! Interesting that your actual maths is more of a hobby and the PhD more number crunchy.
I never left maths, although I put it on the shelf for sometime as I thought Sympy was better than I'll ever be and I was always a wizz with coding. Over the last few years particularly I've been buying up very old textbooks (some older than the USA) and working through all of mathematics from first principles; Greek geometry > Arab spherical/projective > Early European > Post-Hilbert > String theory.
It's been a wild ride. There seems to be a fundamental disconnect between what mathematics and physics were before and after Hilbert. I think this, taken to extremes, is why string theory is nuts and practical high energy physics is about numerical approximations. Recall that Feynmann's great insight was "let's integrate this divergent series"; had anyone else said that, they'd be laughed out of academia entirely.
I'm pretty sure we have to peel all the way back to Euler and walk back forward along a different path to fix the mess. Fortunately; Hamilton, Maxwell, and Tait already went far along such a path... although it is overgrown, it can still be made out.
I've gone down it, and it does lead to a whole different world. However, that whole different world has its own traps.
I'm working on a book and/or video series on it. How can I contact you to share a draft when it's ready?
I have wanted to do something like what you are doing, but that will definitely have to wait for retirement. It takes a lot more time to go back to the classics and go down those paths. The Number Theory book by Gauss is a case in point. I would love to work through it, but those are some difficult pages. I need a full time effort for something like that.
This channel needs an email, let me go get one and I will post it here as well as more broadly.
May you please describe what you mean by “analysis”, I hear it used a lot but have yet to find a nice definition. I will go look, but I hope you can answer my question.
So Analysis can mean to analyze data as I did during my graduate work, but in mathematics (and I thankfully have gotten to read and learn a lot of analysis) Analysis is Mathematical Analysis, which is really "Calculus but with everything proven" or "All the proofs that show us that Calculus works." Here is the Wikipedia article:
www.wikiwand.com/en/articles/Mathematical_analysis
Mathematical Analysis has many branches (Real, Complex, Functional, Fourier, Harmonic,...)
Does that help?