I studied statistics and the Law of Large Numbers is honestly mind boggling. I mean, I understand that it’s true and I’ve studied the proof, but it’s still enormously counterintuitive. It’s not surprising that anyone who isn’t familiar with it (which is the vast majority of people) to have no understanding of this phenomenon at all.
Intentionally blank page: Many documents contain pages on which the text "This page intentionally left blank" is printed, thereby making the page not blank
Thats not a paradox. The pages are blank in terms of the topic of the book, and the note is to inform you that it’s not a mistake.
It’s not particularly confusing, but there are a whole class of paradoxes that rely on the same mechanism – the truth of a statement is being altered by the existence of the statement, because it is self-referential in some way.
I think that the Berry paradox is the first one of these that I ran into, and it’s a little more confusing to most, I think.
Probability is a big one for me that I can’t wrap my head around because the rules just don’t seem to line up with reality. Like, if I roll a die 10 times and get 6 all 10 times, what is the probability of me rolling 6 again the next roll? It’s 1 in 6. But that’s insane. I just rolled 6 10 times in a row. That’s so wildly unlikely, it feels wrong that the odds I’d roll 6 again are only 1 in 6.
Unintended consequences. People like to propose grand schemes that will "fix everything", but refuse to accept that there are downsides to that grand scheme.
That “…” means “it continues to the infinite”. And yet when you show this reasoning to people, they keep “looking” for the last 9, to claim that 0.999… is not the exact same as 1.
And that applies to all humans. You might counter it rationally, you might train yourself to recognise “it’s infinite, so theoretically it’ll behave in a certain way”, but you don’t grasp it. I don’t, either.
In this case you literally divide 1 by 3. And that's 0.3333 . And if you multiply 1/3 by 3 you get 1 and if you multiply 0.3333 by 3 you get 0.9999. So these two are the same.
Just pretend I added dots. But that still doesn’t change anything?
Imagine a pizza, I can divide that pizza into halves, thirds, quarters, etc. because conceptually they represent splitting a defined thing into chunks that are the sum of its whole. 1/3 can exist in this world of finites.
0.333… is unending. I can’t have 0.333… of a pizza, because 0.333… is a number and that makes as much sense as saying I’ll have 2.8 pizza. Do I mean 2.8 times a pizza, 2.8% of one? Etc.
1/3 being equal to .333... Is incredibly basic fractional math.
Think about it this way. What is the value of 1 split into thirds expressed as a decimal?
It can't be .3 because 3 of those is only equal to .9
It also can't be .34 because three of those would be equal to 1.2
This is actually an artifact of using a base 10 number system. For instance if we instead tried representing the fraction 1/3 using base 12 we actually get 1/3=4 (subscript 12 which I can't do on my phone)
Now there are proofs you can find relating to 1/3 being equal to .333... But generally the more simplistic the problem, the more complex the proof is. You might have trouble understand them if you haven't done some advanced work in number theory.
I get its basic shit that’s over my head. I’m just trying to understands
If the only reason is because 1/3 of 1 = 0.9, than id say the problem is with the question not the answer? Seems like 1 cannot be divided without some magical remainder amount existing
If I have 100 dogs, and I split them into thirds I’ve got 3 lots of 33 dogs and 1 dog left over. So the issue is with my original idea of splitting the dogs into thirds, because clearly I haven’t got 100% in 3 lots because 1 of them is by itself.
Likewise would 0.888… be .9? If we assume that magical remainder number ticks you up the next number wouldn’t that also hold true here as well?
And if 0.8 is the same as 0.888888888…, than why wouldn’t we say 0.7 equals 0.9, etc?
It’s over the head of everyone. That’s why I shared it here.
Likewise would 0.888… be .9?
No, but 0.899… = 0.9. This only applies to the repeating sequences of the last digit of your base. We’re using base 10 so it got to be 9.
If I have 100 dogs, and I split them into thirds I’ve got 3 lots of 33 dogs and 1 dog left over. So the issue is with my original idea of splitting the dogs into thirds, because clearly I haven’t got 100% in 3 lots because 1 of them is by itself.
Then you split the leftover dog into 10 parts. Why 10? Because you use base 10. Three of those parts go to each lot of dogs… and you still have 1/10 dog left.
Then you do it again. And you have 1/100 dog left. And again, and again, infinitely.
If you take that “infinitely” into account, then you can say that each lot of dogs has exactly one third of the original amount.
Is there a number system that's not base 10 that would be a "more perfect" representation or that would be better able/more inherently able to capture infinities? Is my question complete nonsense?
Different bases would have different things they cannot represent as a decimal, but no matter what base you can find something that isn't there.
For real world use base 12 is much nicer than base 10. However it isn't perfect. Circles are 360 degrees because base 360 is even nicer yet, but probably too hard to teach multiplication tables.
No, because that "some point" will never happen. There is no last nine to round up, because if there were a last nine, they wouldn't be infinitely many.
There are many different proofs of this online, more or less rigorous.
.333... Is a third. That's just a quirk of base 10. If you go to a different number system you won't run into that particular issue.
The most common other base people know of is binary. Base 2. So in binary the fraction would be 1/11 and then 1/11(binary)=1/3(base 10).
I remember talk back in the day that base 12 is good for most common human problems. Some people were interested in trying to get people to switch to that.
1/3 of 12 is 4.
So 4/12=1/3=3.33333.../10
.333... Is just the cursive way of writing 1/3.
I still don't "grasp" infinity. I'd recon you'd need an infinite mind to grasp infinity.
It's like when people come to America and are surprised when tax isn't included in sale prices. The .0333... you forgot to add on will get you in trouble with the universes math IRS.
One way to tell if two numbers are equal is to show there’s no real number between them. Try to formulate a number that’s between 0.999… and 1. You can’t do that.
0.999… means infinitely repeating 9s. There’s no more 9 to add that hasn’t already been added. If you can add another 9, then it’s not infinitely repeating.
Because it isn’t 0.9; it’s 0.999… with the ellipsis saying “repeat this to the infinite” being part of the number. And you don’t need to round it up to get 0.999… = 1, since the 9 keeps going on and on, so their difference is infinitesimally small = zero.
Another thing showing that they’re the same number is that there is no number between them. For example:
0.9 (no ellipsis) and 1 are different because 0.95 is between them
0.95 and 1 are different because 0.97 is between them
there’s no number between 0.999… (with ellipsis) and 1, so they are the same. inb4 no “last nine” because it’s infinite.
In the real world when you see .9 you often should round it. You rarely have as much precision as presenting - .5 should generally be seen as 1 unless you have reason to believe the measurement is that precise.
0.999… means the value of the limit of a sequence {0.9, 0.99, 0.999, …} as number of 9s (or length of a sequence) goes to infinity, and the limit is very clearly 1 in my mind.
That why someone behaves a certain way is only important inasmuch as it determines whether they’ll keep behaving that way.
Examples:
Criminals don’t need to be punished but rehabilitated; because blame and guilt aren’t important; recidivism is.
Your lover might have all sorts of reasons they love you, and some of those may seem very romantic and some might seem as unromantic as can be. But as long as they will keep living you, that’s what’s important.
Everybody else is saying things that some humans are too dumb to grasp. I’ll give you an example that virtually all humans are too dumb to grasp.
How are our decisions affected by conflicts of interests? The last time I looked into this, the research in this area said that humans virtually always underestimate the effect that a conflict of interests has on them, by a lot. Many people don’t even see the conflict of interests. People who recognize the conflict of interests believe that because they are aware of the conflict of interests, they can mitigate the effects completely. They are wrong.
Humans get entangled by conflicts of interests just like dogs get entangled by their leashes. Just like dogs, many times, humans don’t realize that they’re caught. Just like dogs, even if you show a human the problem, they cannot understand. But even worse than dogs getting tangled by their leashes, humans believe they can understand what to do when they’re caught up, but it turns out that they’re wrong.
The existence of poverty/hunger/homelessness in a post-scarcity world. if we wanted to eliminate those problems we could, but humans are blocked on how it can be done without hurting their own wealth.
We're not yet in a post scarcity world. We're tantalizing close, but not quite there yet.
There are three main areas we need to work on.
First is power generation. We need more, and it needs to be decupled from fossil fuels. Nuclear is the obvious answer for massive amounts of power output without using massive amounts of land, but fossil fuel lobbies have been hamstringing development since the 50s.
The important thing here isn't just replacing fossil fuels. That would just leave us were we are now. No we need to double or triple world power generation as a start.
The second area that needs work is connected to the first. Transportation. Not just electric cars, but container ships and trains and everything in-between.
This is where that added power generation comes in. We need to make it basically free to move things from point A to point B. There are some ways to do this, particularly for container ships. But we need the raw power available before they become viable.
The final area is automation. We need more. Once people need to be put out of work in massive numbers. We need to decuple work from life.
That final step is the hardest with the most pitfalls. It will happen. Well, the automation and unemployment will happen. After that we can either spiral into a hell scape or rise above into a post scarcity utopia...
It really depends on when and how the guillotines come out
You’re right, and I suppose I was half-thinking along the lines of “we have all the pieces to solve this, but we don’t because we’re frozen in place by greed” instead of “this is something we could do with infrastructure today”. If everyone could collectively let go and re-distribute wealth and materials efficiently everyone would be much better off for it, but instead we’re stuck in some game theory hell where the optimal personal choice results in one of the worst outcomes.
Under capitalism, food isn’t produced to eat but to make profits. When it’s not profitable to sell, they will rather dump foods, starving the people rather than to plainly donate. We produce enough foods to feed the entire population. But the sole purpose of food is to not feed the people, but to feed the greed of the producers, the farmers, the corporates. Capitalism created an artificial scarcity of food where we produce too much food for the obese and throw the rest away to rot in front of the poor.
I study a lot of geopolitics and history and I have read of many different aid programs, domestically for citizens or abroad to poverty and war stricken countries.
Unfortunately it’s not as easy as dumping a bunch of money, food or whatever resource into the problem. For example there are cities with tons of homeless shelters but many stay on the streets. There are massive teams of social workers dedicated to helping people in need but many of them refuse their help.
When it comes to countries sometimes this aid is embezzled and only given to those loyal to the government. Sometimes used to fuel armies to continue conflicts, or just disappear into corruption and resold by crooked politicians to make a profit. Additionally it can hurt local, and in turn, the wider economy. The aid distributed for free kills many local businesses and livelihoods because you can compete with free.
Especially when you have some stupid company pulling a publicity stunt to send their own products as aid to struggling countries. One example was this brand of shoes that would donate a pair for every pair sold. This “friendly gesture” killed off all local cobblers, shoe manufacturers, shoe stores and prevented anyone from doing so to make a living, not to mention preventing self sufficiency of the country. That’s just one example, there are a lot of companies and misguided companies that do exactly this and many economists recommend that these poor countries should refuse this aid.
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