There are many equivalent definitions and many of them do not refer to geometry at all. If you don't want to go through cos you can always define pi as sqrt(6 * sum from 1 to inf 1/n^2).
You can also define it as `3.14159...` just because. Obviously, a π definition entirely divorced from geometry becomes irrelevant to it - instead, in geometry, you'd still use π = circumference/diameter, or π = whatever(cos), and those values would happen to be the same as a non-geometric π, but only if the geometric π is the one from Euclidean geometry.
Mathlib defines cos x = (exp(ix)+exp(-ix))/2, which is not a definition via Taylor series (even though you can derive the Taylor series of cos quite easily from it). exp is defined as a Taylor series in mathlib, but it might just as easily be defined as the unique solution of a particular IVP, etc. Regardless of this, I have no idea why to you seemingly a definition via Taylor series is not a "true" definition, you could probably crack open half a dozen (rigorous) real or complex analysis texts, they're likely to define sin and cos in some such way (or, alternatively, as the single set of functions satisfying certain axioms), because defining them via geometry and making this rigorous is much harder.
I can't argue whether cos has a "geometric nature" or not, because I don't know what that means. Undoubtedly cos is useful in geometry. It is, however, used in a wide range of other domains that make absolutely no reference to geometry. mathlib's definition of cos doesn't import a single geometry definition or theorem.
Remember that the starting point of this discussion was that somebody was claiming that "pi is different in non-Euclidean geometry", which, no, even in a completely different geometry, the trigonometric functions would be useful and pi is closely related to them.
I am not understanding why you think this is at all relevant.
Its like saying a^2 + b^2 = c^2 is not geometric because it doesnt make reference to triangles. But at the end of the day, everyone understands Pythagorean theorem to be an inherently geometric equation, because geomtry is just equations and numbers.
I realize to some extent this is all subjective, but to me its insane to claim that cos is not an inherently geometric function. Agree to disagree.
You're analogy is flawed. Pythagoras' theorem is about right triangles. "a^2+b^2=c^2" isn't about triangles, it's not even a theorem, it's simply an equation (typically a diophantine one) that is satisfied by some numbers but not others. Something which typically belongs to number theory. Obviously the two things are closely related (which is the beauty of mathematics - there are a lot of connections between very different fields).
But really, I'll refer again to the part of my previous reply where I contextualise why I wrote what I wrote and how that answers the question of whether pi is somehow arbitrary due to the fact that we usually think of space as Euclidean: it's not.
Drip irrigation is a once and done setup and also automated. I feel like this project is insanely cool, but ultimately not practically useful at the pricepoint.
Watering is definitely a solved problem in agriculture. There is absolutely no scenario where two plants growing right next to each other would need drastically different amounts of water. The project, founders and company are utterly useless.
Not true. I pretty much align on the liberal side of every issue, but well, I hate yalls smug bullshit and metapolitics. Im sure this feeling isnt uncommon, this thread is a great example why.
So you're willing to vote against your interests and beliefs because some people on the left are smug? Interesting take, I'm glad you've found the right with their total lack of smug people.
I think the rhetoric and metapolitics the left is engaging in is dangerous, this event case in point. Do I have to quote the people in this very thread calling him proto-hitler?
Also seeing you smug asshats, here and in real life, taken down a notch is very much in my interest.
That seems self defeating, nose meet knife but I guess if you're willing to give up what you actually want for the sake of annoying strangers that is your right. Doesn't seem like a recipe for happiness though.
Yeah, if stuff like that is enough to make you vote against your own interests I honestly don't know what to say except I struggle to believe those are actually your honest beliefs.
I don't like a lot of people on the left in politics but that is not enough to make me want to vote against my interests/beliefs. I don't like you so I'm going to shoot myself in the foot is just dumb.
Isn’t it possible to dislike woke and MAGA but realize woke has real institutional power over everything today and is a corrupt and unmeritocraric set of ideals. Where as MAGA has no real power or influence in anything of consequence and is therefore benign compared to woke.
Is it wrong? Does the right not control the supreme court, senate and house? How about the media? The largest tv news channel is right, basically all popular talk radio is right, the largest newspapers?
How many state governments are run by the right? What are the QoL stats like for those states?
You think Corporations are left wing? Tech employees might lean left at least the more vocal ones but corporations are definitely not left wing for the most part. Media and Academia I can accept and I already mentioned journalism or at least news which clearly favours the right.
Yeah, corporations are clearly left wing with few exceptions. They may not be your brand of left wing but they clearly are left wing. Blatantly so. Dont gaslight.
3.4% of journalists are republicans while 34% are democrats. The reason fox news is the most popular is because its the only mainstream conservative news in the U.S. in a sea of liberal media. The vast majority of journalism and journalists lean left.
Oh of course sorry, I forgot that social media managers are required to be completely honest about their corporate positions when making social media posts latching onto social trends.
I honestly think you might be the first person I've ever spoken to that has fallen for this stuff.
> Oh of course sorry, I forgot that social media managers are required to be completely honest about their corporate positions when making social media posts latching onto social trends.
Yes, congrats on being the only person in the world to believe a corporations social media posts around social issues.
>I'd like you to prove it now, or are you going to claim everyone you don't like isn't part of the true left?
I'm not sure what you're asking of me here? Lots of people on the left I don't like and lots of people on the right I disagree with on a lot of issues but like. My views are very socially liberal, financially I want everyone to have a very strong airtight safety net and access to the essentials for a safe healthy life, but I am also very pro capitalism.
I don't like any corporation though, they are made up of people and can change completely in an instant where excepting a mental health episode individuals aren't like that.
Sign me up for the not uncommon club because you echoed my sentiments exactly. :D
The left has made it impossible to resonate with them as a liberal. They've been as anti-resonant as can be but somehow getting even worse with every passing news cycle.
If nothing had happened over the last few months (even taking into account the last few years and their totalitarian grip over all tech), Biden would begrudgingly still have my vote, though it was hanging by a thread. Then enter Putin-esque lawfare fueled by a fear campaign, the dementia reveal in the debate, lefties mourning the near-miss... "B-but he's gonna be a dictator!!" Lol. Even if that's true, the left brought it in themselves, and it'd be schadenfreude. Be afraid! Be very afraid!! https://m.youtube.com/watch?v=ofIlP1gJ-Ho
The observation that there is a (very) strong statistical correlation between cranium and social size is an interesting and correct observation.
That much is true and uncontroversial.
What the article takes issue with is the exact number of 150, which can vary from person to person. But really, the criticism entirely misses the point. The number is just a rule of thumb derived from extrapolation. It's not a hard and fast rule like "You can only have 150 friends". Obviously.
Perhaps it should be something like cranial volume / body volume, or else we'd expect whales and dolphins to have massive tribe sizes, yet they typically hang with something like 20 peers.
Doctors are often on call 24/7 and do significantly more work than the average C-suite, yet you're complaining about a two hour work day?
The lack of self awareness is astounding.