Perhaps, also do at least the 23andme test.

No it doesn't.

But let me propose that we restrain oil cars to specifically designed race tracks in the future and keep streets that are meant for transport and travel automated and electric. That way we can have the best of both worlds while minimizing the down sides: pollution and accidents.

Wait, a Peugeot?
Unacceptable.

So we're cool with providing platform to proposals for murdering babies and wiping out this or that class as long as some PM pushing is sprinkled along the way? cause you know not allowing someone to push their propaganda on a BTC forum would be like communist censorship and such  

My ignore list of people quoting idiots got to a point where i just see full pages of ignored users

Sure you'll be able to afford any of that once you've settled your gambling debts?

^damn son 24 seconds!


Hasn't Calvin also got a murder accusation hovering over him? Can't keep up tbh.

Same.  Pity that the masses don't see the agenda. There's still loads who believe terrorists took control of 3, 747's with box cutters and performed impossible maneuvers.    

stamp data, log scale, puts the bear line at 42

can you guys f***ing tell me what about you're talking??  

As for a "beginner level" introduction, I'm not really aware of any that isn't gritty rigorous Math. And in that case any would be as good as any other I suppose, since the definitions are always the same (except for perhaps the symbols used). If you feel like digging deeper I'm sure you'll find any number of resources on Google. All my notes and books for these topics are in non-English though, so I can't recommend you any reference here. But alas.


Assumptions are created out of more or less thin air. Generally based on past experiences (I'm not sure if we can arrive at any assumption without making references to previous ones, which is a problem in and of itself). It's also not exactly that numbers "are" a finite field, they can be depending on how many you have to play with. The numbers we usually use are not a finite field, you always have a unique "+1". However.


In the case of finite fields, if you want to go from the "human experience" side you could think of it like this.

If you think that infinity exists, then there's not much reason to argue here since you can just keep adding numbers and always get a unique new one, so 1+1 will always be 2 in that world.

If you however believe that infinity can't exist in reality, then the only conclusion is that any field of numbers must be finite, because you'll eventually run out. And in that world you eventually come full circle, otherwise you can't have a number field that functions in the way we understand numbers. It is the only way to formalize our natural understanding of numbers (that I am currently aware of).


As for what fields are, here's a very brief overview that leaves out a fair deal of the gritty parts that are necessary to formalize this. But this should hopefully give somewhat of a more formal intuition that you could compare against our natural intuition.

A field can be any set of numbers that satisfies a few properties. The most important ones for the topic we're having are the existence of a set of elements (or numbers), the existence of two operations (e.g. addition and multiplication), the existence of a neutral element for each operation, and the existence of an inverse element for each operation.

Let's take {0,1} as the set of numbers. And addition and multiplication as its two operations. The operation "o" (+ or *) now has to ensure that each element has a unique inverse element. So if you take any element X , there must be another element Y such that X o Y spits out the neutral element regarding "o". For addition this is 0 (you add 0, shit happens), for multiplication it's 1 (you multiply by 1, nothing happens). If you think about it, whenever you invert a number you get its neutral, 3 * 1/3 = 1, 3 + (-3) = 0.

If these properties are violated you can somehow show that the whole natural intuition of numbers just breaks down, but I can't think of a good example on the spot. Been too long since I've done anything in this area.


In the usual fields the inverse element would just be -X for addition and 1/x for multiplication. In this finite field you can't do this, because "1/1" clearly does not exist as neither does an element called "-1".

However, with the circular arrangement you can quickly see that:

0+0 = 0
1+1 = 0

0*1 = 0
1*0 = 0
1*1 = 1

Hence, each element has an inverse regarding multiplication and addition, and our intuition still works. This way to look at it satisfies the requirements of a field. It just so happens to be finite. This curiously doesn't work for any set of numbers either, the number of elements has to be infinite, a prime, or a prime power.
If you want to get technical, then "2" in the way we normally understand it won't give you "2+2 = 0", but there is an abstract field that extends {0,1} in a way such that the elements that you could "call '2'" would satisfy 2+2 = 0. You can easily get 2+3=0 for {0,1,2,3,4} with the usual addition though (check this yourself if you'd like as an exercise).


As for 'why' this works, I doubt anybody knows. Emergent properties?

Essentially, fields are merely a formalization of the way in which we naturally came to use numbers based on our experience of reality. And the formalization naturally gives rise to both finite and infinite fields. There are also weird fields that have polynomials as their "numbers" and where "1" is suddenly a polynomial (the constant polynomial 1). But you would never expect either of these by not carefully thinking about the fundamentals, what you already know, the implications of either, or what other ways you could view what you already know in.

These weird mysteries are why I'm against quickly rushing to conclusions on any subject and prefer looking for as many explanations and vantage points as I am currently capable of. The universe has a way to always screw us when we think we "know", and to reward us with new exciting experiences if we remain open.

Honestly it's never to late, especially if you're interested.

When I was doing my Bachelor there was a guy well into his 50s or 60s who was taking all the "real" Math lectures with us as opposed to the dumbed down ones for Economists etc. People were very welcoming towards him and he seemed to be enjoying himself quite a lot. I changed universities throughout my Bachelor to the next city. And found the same guy taking Master level lectures at the new place when I was a bit later (first place was for Economics and Business with focus on Math, second had a proper full blown Math department). So clearly he didn't just attend, he was doing quite well too. And that appeared to be his first time at university in his life as well.

And older people have the big bonus that they may not have to perform or prove anything. You could just study for the sake of it, which takes all the stress away. And their life experiences can make it easier than for most young students who are still trying to figure out what the fuck is going on with life in the first place.


Be prepared to feel like a complete idiot as you start out, should you choose to do so though. I have not met anyone who didn't at least throughout the better portion of the first semester. But even those come back years later and still find new things they had not considered. The very first minute of the very first lecture that I took I almost fell into despair just looking at the blackboard.

Anyway, not trying to shill you into anything here. But the option is there and worth considering. Especially for those with an appreciation of just thinking about things they don't need to for nothing other than the sake of doing so. There are very few ways that are similarly efficient in breaking down all of your preconceived notions as studying Mathematics. Notions such as regret for example.

Also that powerwall thingy is still pretty expensive. If you can afford to pay the premium for the privilege of being completely self sufficient then great. For me, a couple of years or maybe a bit more and I will be there.

So maybe not already there... but almost.

Can always charge batteries with electricity generated from nuclear power while transitioning to solar and fusion. The transition also won't be nearly as bad as you make it out to be if it's a necessity. Necessity implies disproportional profits, which from your perspective the Jews would be so happy to provide that they'll make it work. If they don't they'd be stuck with little to nothing and a lot of mostly useless money.

Much to early but I like where your going with this...tell us more.