vacuumcl
Joined 4 years ago
Joined 4 years ago
But maybe you do, and I am seeing patterns in sand.
- The cardinality of the odd and even integers is the same.
- It is true there are more points on a plane then on a line (Cantor's theorem.)
- The circle is the compactified real line, i.e. it can be represented as the real numbers with one additional point (the point at infinity). In terms of cardinality they are the same since they just differ by one point which does not change the cardinality.
- There are not more points on a plane than a half-plane, you can find a bijective mapping between them easily.
- There are more rationals than integers: not true, they are both countable sets of the same cardinality.
- There are more reals than rationals, this is true (again Cantor.)
You've got to push past it, though, and take the plunge to ask people out even if they might reject you or even if it might break some social norms. I just got out of a long-term relationship and am also approaching my thirties. When I met her, she was my housemate during university years. My other housemates and friends said it would be inappropriate to make a move, but I went for it anyway, and it gave me 9 years of happiness.
As another example, I googled some project Euler solutions in Mathematica and (pure Python) and found this: https://www.nayuki.io/page/project-euler-solutions. Compared to the pure Python solutions, the Mathematica code is typically much smaller. Of course this is not Sympy, but a lot of the Python syntax carries over to SymPy as well.
In any case, I think a big barrier to starting things can often also just be the fear of failure or of wasting time. I spent a lot of time making electronic music as a hobby, and am probably better than most people at understanding and playing music, but for music to play a meaningful impact in my life I would need to put in a lot more work still.
On the other hand, I studied physics and mathematics far beyond the average person (getting a PhD and publishing multiple papers), but I had the support of the university and the academic environment to give me that extra push to do it.
There are so many things I would like to pursue in my free time. Building a small startup, writing a book, making YouTube videos, etc. I know that the most important thing is to just start, but the decision paralysis, and uncertainty about whether it will work out in the end can definitely be a barrier, since I can also just go out with friends and enjoy my life instead of spending time solitary.