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## There are no facts in the future

Fact-oriented behavior is considered rational and methodical by many, especially technocrats. But facts exist entirely in the past. The human future is composed of what we intend to do, what is likely or probable, what we assume and what we believe. The human future is completely devoid of facts. When this simple fact is ignored, it has a huge effect on how people (even technocrats) launch initiatives. People often fail to distinguish between "that's how things are" and "that's how they have been in the past". Shaping the future requires abandoning fact oriented thinking EXCEPT to the extent that facts from the past can shape our assumptions and beliefs. We can look at Oklahoma tornadoes from last week (i.e., a fact) and create an assumption "I should build a better basement shelter" or "I should leave Oklahoma". Neither of these has any facts but the divergent assumptions have a huge impact on the person's future. The tornado doesn't know the difference and doesn't care.

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## Time Traveller

In terms of people, you are right, there is no certainty for what is our future. Though that said, I do believe that our futures are created from our actions of today. There are too, exceptions as well. These are not readily explained, however, it has been recorded that some people will get visions of a future event before it happens. As time unfolds, that vision transpires and so effectively they have foreseen a future fact!

I agree that shaping a future does to an extent require letting go of the past, as otherwise you keep getting the same result if you keep doing the same thing. To shape something differently new ways of thinking need to be incorporated and old ideas challenged, with the hope of making new innovations and creations.

All of us live only in the present and as such because the future is always out of our reach it is empty! :D

## Casey Christofaris 10+

http://www.ted.com/conversations/13925/is_our_math_wrong_is_it_our_a.html

## Time Traveller

## Casey Christofaris 10+

Also check out that ted talk it is all right there

## Casey Christofaris 10+

Our maths aren't wrong, its reality itself that defies definition. For example, why is the result of a division by zero is undefined? The reason is the fact that any attempt at a definition leads to a contradiction.

To begin with, how do we define division? The ratio r of two numbers a and b:

r=a/b

is that number r that satisfies

a=r*b.

Well, if b=0, i.e., we are trying to divide by zero, we have to find a number r such that r*0=a. (1)

But r*0=0

for all numbers r, and so unless a=0 there is no solution of equation (1).

Now you could say that r=infinity satisfies (1). That's a common way of putting things, but what's infinity? It is not a number! Why not? Because if we treated it like a number we'd run into contradictions. Ask for example what we obtain when adding a number to infinity. The common perception is that infinity plus any number is still infinity. If that's so, then

infinity = infinity+1 = infinity + 2

which would imply that 1 equals 2 if infinity was a number. That in turn would imply that all integers are equal, for example, and our whole number system would collapse!

So, what now? How about 0/0?

I said above that we can't solve the equation (1) unless a=0. So, in that case, what does it mean to divide by zero? Again, we run into contradictions if we attempt to assign any number to 0/0. Let's call the result of 0/0, z, if it made sense. z would have to satisfy:

z*0=0. (2)

That's OK as far as it goes, any number z satisfies that equation. But it means that the result of 0/0 could be anything. We could argue that it's 1, or 2, and again we have a contradiction since 1 does not equal 2

## Casey Christofaris 10+

But perhaps there is a number z satisfying (2) that's somehow special and we just have not identified it? So here is a slightly more subtle approach. Division is a continuous process. Suppose b and c are both non-zero. Then, in a sense that can be made precise. the ratios a/b and a/c will be close if b and c are close. A similar statement applies to the numerator of a ratio (except that it may be zero.)

So now assume that 0/0 has some meaningful numerical value (whatever it may be - we don't know yet), and consider a situation where both a and b in the ratio a/b become smaller and smaller. As they do the ratio should become closer and closer to the unknown value of 0/0.

There are many ways in which we can choose a and b and let them become smaller. For example, suppose that a=b throughout the process. For example, we might pick

a=b = 1, 1/2, 1/3, 1/4, ....

Since

a=b,

for all choices of a we get the ratio 1 every time! This suggests that 0/0 should equal 1. But we could just as well pick

b = 1, 1/2, 1/3, 1/4, ....

and let a be twice as large as b. Then the ratio is always 2! So 0/0 should equal 2. But we just said it should equal 1! In fact, by letting a be r times as large as b we could get any ratio r we please!

So again we run into contradictions, and therefore we are compelled to

let 0/0 be undefined.

So, yeah, zero does not exist, unless if you studied calculus and learn about Rule of L'HÃ´pital. Which then gets pretty whacky and my hands are all tired from typing and steering this spaceship at the same time so I am ashamed to tell you to just Wikipedia it. Sorry.

## Ashwath Nityanandan

## Casey Christofaris 10+

## Arkady Grudzinsky 50+

Mathematical "facts" are not facts, they represent ideas. What these ideas represent in reality - is up to us. 1 box of tea may have 6 packs inside, each of them has 20 small bags. So, when you say "1", it can be any number.

Without context, there is no meaning.

"Arthur: Six by nine? Forty-two? You know, I've always felt that there was something fundamentally wrong with the Universe.

(Faint and distant voice:) Base thirteen!"