I'm somewhat obsessed with this notion of scale. The scale of the universe seems to be expanding as we are discovering more and more and more and more of it. It never ends. Unless extinction level events happen or entire groups are wiped out, knowledge continues to expand, rather than retract. We smirk at the silly "technology" of the past and what people believed even 200 years ago. The smart phone culture is only 9 years old. What do we think the philosophy and technology of a progressed Earth will look like in 2216? What will they be able to detect, calculate, or philosophize? Maybe it's the morning sativa but it just wouldn't shock me to one day find out there are far more dimensions. Maybe it's not 4, maybe it's 40, maybe infinite. We just don't have either the technological, and/or biological tools to detect them. Videos like these make such notions very plausible to me.
Both, and neither. They're in constant motion.. so from one point to the next, I highly doubt they are in a position where they can be considered going in a curve or a straight line. Maybe if you could take a snapshot of a wave, you could see its movement and say "this movement will create a curve or line".. but the moment right after the snapshot will have different qualities that don't match your snapshot.
For the repeating 9 topic: this, in my opinion, is the best demonstration of the proof. It requires a limit.
Over my head. From what I can tell this shows .999... =1. But requires the repeating 9's to have an end/limit?
Yeah.. some of the proofs for showing why 0.99... is the same as 1 is beyond my mathematical grasp.. but here is another way to look at it. Numbers are but values.. and in mathematics, 0.9 repeating has the same value as 1. Think about the real world.. say you have 1 penny. To you, it has the value of 1 cent. You then take that penny and make it your control penny. Then you get another penny and compare the 2. Compared to the 1st penny, it had one less atom than your control penny. So in reality, your 2nd penny is really only 0.99... pennies, but the value is still one. Same thing if you hold up 1 finger. You say you're holding up 1 finger.. then you put it down for a second and put it back up, you still say you're holding up 1 finger. But is it still really one? From the first time you put it up to the second, the composition of your finger changed. You might have more or less energy and matter in it.. so technically it is no longer a whole, even 1 in comparison to your control finger. That's how numbers are.. they are simply a value that we place on something, even different somethings. So in math and even reality, 0.9 repeating has the same value as 1.. in the same way that 0.38+0.62 has the same value as 1.
And if you had 0.999 with an extra thousand 9s on the end.. if it were not a repeating number, it wouldn't be equal to 1 because you can add value to it to get to 1. There is no value that you can add to 0.9 repeating to get to 1.. in the same way there is no value to add to (0.24+0.76). The reason you can't add value to get to 1 from 0.9 repeating is because they're the same value.
I would argue you cannot add to .9 repeating because it is a fictitious valueless symbol. As his equation above, deals with infinity, and you know I take issue with that. No psychobabble will convince me they can incorporate infinity and come out with an actual value. Renormalization as you recall.
Well it's silly to think there aren't things in this universe that aren't infinite.. as to what, that's up for debate. So renormalization is something that will be needed for certain things. As for that specific proof.. if you didn't like it due to infinity, there are probably at least 10 other proofs out there that demonstrate how 0.9 repeating is the same as 1 without the use of infinity. 0.9 repeating is 1 in the same way that uno and ein are one. You don't need any formula to see that.. yes, it is a fictitious value.. as are all our numbers. They're just verbal labels for a value.. that's all 0.9 repeating is, another label for 1 the language of math. Repeating numbers are needed, as somethings when split.. don't form easy splits. Like 1/3.. or 0.3 repeating. The cool thing about it is you can get as precise as you want. If you wanted to split something up by weight, you can use 3 decimal places.. not that you'd need them, but even 20 decimal places. Imagine if you and 8 friends split an ounce.. but your scale only goes back 1 decimal place. You'd each get 3.1 grams.. but between 9 people, adds up to 27.9 grams. So you'll have 0.1 grams leftover.. and everyone wants it. Greedy bastards.. but if you have a scale that went down more decimal places, you'd each get 3.1111111 grams.. leaving only 0.0000009 grams leftover, which is truly next to nothing and no one complains. That was a dumb example.. but just shows how repeating numbers can be nice when splitting something uneven. 1 isn't always the easiest to split either.. which is why 0.9 repeating finds use in taking its place.
oh my brain.... what if strings quarks or whatever the smallest unit we can detect, is another massive universe? And our universe is a quark? Sigh