For politicians? Zeno's Paradox would probably give you the best answer where the distance between here and the truth is subdivided into infinity.

The BBC's Robert Peston has written an article that echoes your confusion (and mine). I don't always agree with what he says, but there's not much to argue in that article.

I think Galbraith is right on the money, the only choices for Greece are capitulation or exit.

I leave you with this - http://www.bbc.com/news/magazine-33346743 - the BBC Magazine advises Greece to follow the teachings of Zeno of Citium, the Stoic. I showed that article to my younger son actually, who's a bit prone to dwelling on past failures and would do well to follow the Stoic principle of only worrying about things that you can change and not those you can't.

Is every good pizza place called Gino's or Zeno's or something that ends in o's ??????????

You're right on two counts: first, I did think you were arguing against the point made; and second I shouldn't have insulted you. Sorry 'bout that.

FWIW, I dropped out of high school after grade 11, I have no college math except what I've been teaching myself recently, and I used none of it when I figured this out for myself. Everything Vi uses in her vids is high school or even grade school math, and if you trust yourself to do arithmetic, then this proof is accessible. She doesn't even hint that the idea of "limits" from calculus gives a quick solution to her 9th reason, the sum of an infinite series.

Anyway, I'm happy to see then that my original prediction has held so far, and nobody here is starting a stupid argument about their feelings about whether this is true.>> ^entr0py:

No reason to be quite that much of a jerk about it. Not everyone has had as much college level math as you. And presumably her videos are about teaching people who don't already know everything she does.
But if you thought I was making an argument against the idea, you're wrong. Vihart presents it very convincingly. I was just trying to think of the implications.
Honestly after watching that video late at night I could no longer wrap my head around inequalities like X < 1. I used to think that meant X could be a number infinitely close to one, but that doesn't work because infinitely close to one is one (most of the video is about explaining why this is true). So, what is the highest possible number that satisfies X < 1? It seems there might be no sensible way of expressing that boundary, and thinking about it just puts you into a spiral of non-working logic exactly like Zeno's paradoxes. Looking back, at 1:23 she mentions what I'm talking about, but doesn't go into it.
Ultimately, she finds this interesting enough to talk about for 10 minutes, and we find it interesting enough to watch. So why should it evoke rage and insults when there's a chance we might talk about it amongst ourselves?

Messenger, there's no reason to be quite that much of a jerk about it. Not everyone has had as much college level math as you. And presumably her videos are about teaching people who don't already know everything she does.

But if you thought I was making an argument against the idea, you're wrong. Vihart presents it very convincingly. I was just trying to think of the implications.

Honestly after watching that video late at night I could no longer wrap my head around inequalities like X < 1. I used to think that meant X could be a number infinitely close to one, but that doesn't work because infinitely close to one is one (most of the video is about explaining why this is true). So, what is the highest possible number that satisfies X < 1? It seems there might be no sensible way of expressing that boundary, and thinking about it just puts you into a spiral of non-working logic exactly like Zeno's paradoxes. Looking back, at 1:23 she mentions what I'm talking about, but doesn't go into it.


Ultimately, she finds this interesting enough to talk about for 10 minutes, and we find it interesting enough to watch. So why should it evoke rage and insults when there's a chance we might talk about it amongst ourselves?

>> ^Ornthoron:

@charliem No, you are wrong.
Noone says that 0.999 = 1. What is true is that the number written as 0.(an infinite number of 9s), which we can write more prettily as 0.(9), is equal to 1. That means equal. Exactly equal. No equivalence needed.
Bear in mind that we are not talking about a number with a finite number of decimals. If we were, it would be true to say that we could get arbitrarily close to 1 without ever being exactly equal. But we are in fact talking about the infinite sum
9 (1/10) + 9 (1/10)^2 + 9 (1/10)^3 + ...
This is a geometric series of the form ar + ar^2 + ar^3 which according to the convergence theorem has the solution
ar/(1-r) = (9 (1/10))/(9/10) = 1
There, I just proved the equality for you.


Something tending to something isn't the something itself. Something tending toward 1 isn't, yet, 1. We don't live in the land of convergent infinities, we live in today. If you can right down enough .99999's that eventually turn into a 1, then I will accept that proof, otherwise, it is an estimation or an assumption. Unless you don't believe in infinite precision, that is. But even then, your left one something with a fineinte number of 9's that don't converge to a 1. Doing loop-de-loops with infinities, a reality in which humans don't and can't inhabit, is trying to abstract away the real problem...the same problem that Zeno proposed long, long ago.

There is no logical reason to suppose that any piece of matter is "the smallest unit"; it would always be logically possible to see something smaller. The smallest unit of space would be a point, it would have no real dimension to speak of, it is what defines dimension; it is not measurable by any other means, it is that base of all measure. A smallest unit of space is logically necessary for motion and many other things. Without it, Zeno's paradox is maintained. Calculus tries to help us out and estimate things based on an ever shrinking delta, but ultimately, this is still just an estimation. This would also mean that all notions of dimensionality could be flawed. IE, there is no real dimension except for what a brain perceives. 3-d (or 4-d or whatever science calls it next) isn't logically a condition of the universe but a condition of the human mind. This isn't to say that the rules of Euclidean geometry are voided, but it does bring some interesting questions as to how objects exist. Waves would not be contiguous in the strictest scene, nor would circles be true circles. At the smallest level, everything would be aliased like a monitor screen, or even more so contain no "space" and just be a formula. In other words, one of the base principles of matter, that it is extended in space would be voided as the idea of extension in what is a non-dimensional reality is meaningless.

What the smallest unit of space does for us is something magical though. Logically speaking, there has to be a smallest unit of time. The smallest unit of time would be the amount of time an entity can transition itself from one space to another space. With this, a logical "fastest speed in the universe" is created; and as evidence would have it there seems to be just such a phenomena! Without a smallest unit of space or time, it means that logically matter is jumping over entire segments of space because it is the only way one could end up moving. As such, there would be no real understanding of how motion really works. If objects are just jumping from one set of spaces to another motion becomes a great mystery. Anyway, I am rambling again. Once again, I usually don't think about the universe like a scientist. I care little for how things appear, and want to understand how things must actually be. So for me, for things to move, for time to progress, for thing to happen they have to be discrete.