chobytes

Seems kind of pointless. The tech for tracking is widely available and straightforward to use. Has been for decades.

3blue1brown has a great geometric LA series on youtube.

While I appreciate the effort the author has clearly put in here, Im not sure the visualization provides much in the way of practical intuition. These seem to essentially be mechanistic explanations of the rote bits of matrix math.

There are already rich geometric interpretations which provide useful intuition for that generalizes, rather than just demonstrating mechanical details.

Used it for like a year before switching to opensuse tumbleweed. For rolling release Ive found it to be a lot more stable, though some of more obscure packages I use are harder to obtain.

What country are you in out of curiosity?

+1 I find it hard not to read that sort of writing style as condescending.

Classic problem of trying to draw definitive lines between these things. I would guess this is more motivated by the social aspects of academics today than any real issue.

In any event reading the work of philosophers has certainly made me a better thinker and mathematician. Without a broad base of thought one can easily get sucked into many intellectual traps and tar pits. In my case, I found Penelope Maddy and Wittgenstein to be helpful when I was figuring out what math "is".

Maybe Schroder-Bernstein could simplify. Easier to write 2 injections.

There is a general notion of derivations I believe theyre using. Ie anything that obeys the Leibniz rule (fg)' = f'g+fh'.

Its an informative exercise to see how many of the standard rules of calculus can be derived using just this rule.

Ah, I think I see. Open sets are just how we encode information topologically. Theyre sort of the "atoms" of topology; the types of opens sets you have say how the topology behaves.

In particular open sets are neighborhoods of all of the points they contain. This means they contain all the topological information about all of their points.

Closed sets are not neighborhoods of their points in general. Eg [0,1] contains no neighborhood of 0 or 1. Then we would require knowledge of the space around those points to know how a function behaves just on [0,1].

In standard calculus this amounts to "taking the left and right limits".

Does that help?

Can you give an example of what you mean?

The concept of a derivation on types could be interesting... but the notation is a bit much for me.

Differential fields are (as I understand it) a hot topic at the moment. Maybe there is some interesting crossovers.

Congratulations! Ive been following development with your blog/yt for a bit, so Im excited to finally check it out.

Ime its like solving puzzles. Maybe like getting really into Go or some similar game.

Fuji XEs are nice, small, relatively cheap bodies with interchangeable lenses. If youre looking for something small and know how to (or are willing to learn to) use a camera, thats what I recommend.

If portability is not a concern, you can pick up used high end Nikon DSLRs and F mount lenses very cheaply right now. Nikon is going all in on mirrorless now so this stuff is "last gen" hence cheap.

Otherwise, just avoid Canon. Theyre becoming increaingly scummy and you probably dont wanna get caught locked into their system.

I got a tiny Fuji mirrorless for my "best camera is the one with you" checkbox too. Next time I catch gear acquisition fever though, I might have to get one of those little Ricohs.

The optics depend so much on physical size that phones have to fake this stuff. Idk why apple doesnt just cut the crap and just release like a m43 with swappable glass rather than all this silly multiple sensor stuff.

Im surprised by all the folks who always pop into these threads saying theyve replaced their XXXX-expensive-dedicated-camera with their phone. Outside of wide DoF, wide FoV, well lit shots I find my camera and iphone to be pretty incomparable.

If apple starts letting us swap the glass out one day we might be have a fight but currently I just dont see it being one at all.

Yeah Im unsure what the point is. The motivation for CT in programming seems weak.

Eg Stuff about types and endofunctors feels like trivial examples using the jargon just to use it. OTOH discovering the Top->Grp functor in algebraic topology is kind of unexpected and revealing.

Eating super spicy food definitely leaves me feeling kind of drunk. Have met others who have this and others who doesnt believe me/think Im exaggerating.

Its a nicely written post, but I think its a bit misleading. This type of exposition preys on peoples feeling that there must be something deeper going on, but ultimately just kicks a real grasp of math down the road. On the bright side maybe a few more people know of the complex exponential though?

The truth is that there is no royal road. No perfect explanation. Nobody can tell you what a mathematical concept really is. The only surefire route is through experience doing and using math.

If you want to know what these numbers "are"... then simply do more math. I encourage you to squeeze some philosophy in as well. Reading Wittgenstein's lectures on mathematics, after taking my first model theory course, really messed me up for awhile!

A bit of knowledge of optics and photography is enough to know that little sensor with miniature glass cant compete with a dedicated camera. (Eg regardless of 'equivalent' field of view via crop factor, a 50mm and 10mm are going to produce a very different depth of field.)

You can definitely take nice photos with it given the right variables and/or some creativity (as you could with a point-and-shoot a decade ago)... but don't be taken in by their marketing if photography is a goal for you.

At this point I feel like using a stripped down fork of firefox is basically a requirement. There's nothing left of the Mozilla that cared it seems.

I always chuckle when I see some like basic logical steps slapped with "citation needed".

Unfortunately I think 10 page expositions/derivations are the highest quality math and physics pages. I think the wikipedia style is fundamentally incompatible with communicating this kind of information unfortunately.

Agreed. My background is in math... and I find math wikipedia to be appealingly low quality. Both for reference and for a general audience.

Oof. This is one of those not-even-wrong cases in which the misunderstanding is revealing.

Math education is so lacking among people who could really benefit from understanding it. Sad state of affairs.

The wolfram language is kind of irrelevant. I dont think anyone outside of HN and programming language people care about it or how its done.

Mathematica is the star of the show. Its a large collection of specialty libraries and tools, with (mostly) very nice documentation, that all interoperate together well.

I can assure you its widely used by certain fields in academia. Im currently a research assistant in physics at a large lab, and mathematica is ubiquitous.

I think its the addictive nature of cardio. Like I definitely feel like I need to get out there and get my heart going. Takes restraint to rest when I know I need it.

I wonder if we could just induce a little healthy endorphin addiction is less fit people to prime them? Haha