你确定你知道的政治 真理 必然性事件都是对的？
Okay, here’s a question for you:
Imagine you’re at the equator
and there’s a rope tied around the earth
– all around the planet there’s a rope lying flat on the ground –
and pretend there’s no hills or water at the equator
and the rope makes an even circle.
Now we cut the rope somewhere
and we sew on an extra yard of rope.
So now it’s one yard longer than it was before.
Then we evenly pull the rope out around the earth’s surface,
making a perfect circle again.
Question is how far off the ground is the new rope?
So again, there’s a rope lying flat all around the earth,
we cut it, add an extra yard rope somewhere,
and then spread the slack around the earth,
in order to get the rope back into a regular circle.
How far off the ground is the new rope?
Is it a mile off the ground?
Is it a yard off the ground?
An inch, Hardly anything at all?
Almost all of us, when we first hear this question, say:”Hardly anything!”
If the rope came off the ground at all
We think you wouldn’t even see the space in between;
The earth is so big,
what’s a yard across the entire circumference around the earth?
Well keep your chickens in the barnyard，
because actually the Rope would be almost six inches off the ground,
5.73 inches to be exact.
Adding just one yard would essentially leave a tripwire
all around the entire circumference of the earth.
In Kenya, Indonesia, the Galapagos. How can that possibly be?
肯尼亚 印度尼西亚 厄瓜多尔 会如何？
Many people when they first hear this think that’d just be right, Okay.
Hang on little guy.
I’ll show you why in a sec, but first:
This example was made famous by Ludwig Wittgenstein.
A 20th century philosopher from Austria.
He thought that when we think about the rope,
we get fooled by what he would call a picture.
A picture that applies in many situations, but not this one.
When we spread something small over something much much bigger,
the effect is often negligible to us.
Pour a gallon of water into the ocean and the ocean would hardly rise;
The picture works there.
But in case of the Rope things are different.
Remember this old equation?
The circumference, the distance around a circle,
always equal two pi times radius.
Now with the rope at the equator,
we’re basically adding a yard to the circumference
and asking how much the radius increases when we do that.
Since a circle’s circumference is always exactly 2pi
or 6.28 times its radius,
then if you add one unit to a circumference,
you’ll always be adding one over two pi units to the radius.
In other words, how much the radius increases remarkably has nothing to do
with how big the circle is.
So whenever you add a yard to a circle
it doesn’t matter how big the circle is.
Whether you add a yard to a rope around the earth
or a rope around a tennis ball
or to a tiny string tied around a needle,
the circle ends up 1 over 2 pi times a yard further out,
or 5.73 inches.
Now even when people see this proof;
even when you show them the algebra for each individual case,
many of us still remain certain that the rope at the equator
wouldn’t come so far off the ground. But we’re wrong… Ok,
whatever, who cares about this?
There is no rope at the equator.
Well, first it’s just interesting that so many of us make that mistake.
What is it about the human mind or
brain that makes us all reason incorrectly here?
And be so sure?
Second, it’s a reminder of the fact
that even when we’re certain about something.
We’re sometimes wrong.
A reminder that something can seem completely obvious to us
and yet it not even be true.
But the big question is:
what does this mean for many of our
other thoughts and convictions?
Should we therefore be less confident in them?
Should we never be certain of anything? That doesn’t seem right.
Part of it depends on how often this happens to us,
that were misled or captivated by a picture,
or are certain about something but wrong.
Does it happen just in these weird cooked up cases
like the rope around the earth?
Or does it happen in more real-life cases?
Could it happen to us when we think about safe politics?
Or when we contemplate the rationality of other people?
Or reflect on the biggest questions of all about life and philosophy?
For instance, think about the current political debate
in the US about minimum wage.
I myself have thought a lot about that particular issue
and I’m certain that raising the minimum wage is the best thing to do.
But now is it possible I’ve been misled
by a picture in my thinking about that?
Now I want to say”No, of course not!”
When I review all my reasons
for thinking we should increase the minimum wage,
they seem watertight.
But then, that’s what I would have said about all my reasons
for thinking that the rope wouldn’t come much off the ground.
“No way!” you say to me,
Maybe this sort of thing happens to you when you think about political issues, but not me!
也许在你考虑政治问题时 这种事会发生 但我肯定不会
I would know if I were making mistakes in my political reasoning.
I’m careful in my reasoning and honest with myself.”
But here’s the thing,
you probably wouldn’t know if you were making those kinds of mistakes. Why?
Well, think about the Rope again.
The only thing that convinces people about the rope
is the proof from the formula.
The intuition is so strong there
that nothing but the proof would get you to see you were wrong.
But with many things in life –
and here’s the crucial point – there just aren’t proofs!
And so in those kinds of cases where there are no proofs,
if you ever were in a grip of misleading picture,
it’d be very difficult for you ever to see that you were.
Because no proof or formula would be there to convince you.
So put those two points together.
One was sometimes certain about something yet it’s not even true.
And two, there are many topics
where if this happen to us.
It’s unlikely we’d ever realize that it did. So,
how should an open-minded honest person regard her own certainty
in areas where there often no proofs like politics, philosophy,
在政治 哲学 道德 美学
ethics, and aesthetics?
Maybe we should be a lot less confident in our beliefs.
After all, we may be wrong more often than we realize…
Or maybe we should be a touch less confident.
Maybe it’s a sign of weakness to temper one’s convictions,
maybe we should remain certain whenever we feel certain.
What do you think?
你确定你知道的政治 真理 必然性事件都是对的？