Less Wrong is a community blog devoted to refining the art of human rationality. Please visit our About page for more information.

Comment author: Lumifer 26 April 2017 02:42:15PM 0 points [-]

Going the right path isn't always easy

On which basis do you decide which path is right and which is not?

I see a real paradox here, not a curiosum.

Are Zeno's paradoxes also "real"?

Comment author: Thomas 26 April 2017 06:06:31PM 0 points [-]

No. Zeno paradoxes aren't real. Why? You have to have an axiomatic system and inside this system you must be able to prove A & NOT A. Then and only then, there is a paradox.

Then EVERY statement is provable inside this axiomatic system and the system is useless.

Zeno had only "paradoxes". Had he formulated one of his paradoxes inside geometry, that would be something! But he didn't. All Zeno had was his intuition that "you can't do infinite number of steps in a finite time".

For the Russell's paradox inside the Naive Set Theory, that is a different story. Using those axioms one can prove that his B is its own member. And one can also prove that it isn't.

But those Cantor's examples, like the Infinite Hotel - are NOT paradoxes. It is odd, and "paradoxical" if you wish, but that's fine. Had Cantor proved, that this hotel can accommodate exactly 7 guests - and someone else (or Cantor) had proved that this hotel can accommodate exactly 12 guests - that would be a paradox indeed.

Assuming that both proofs were correct.

I know, you know that.

Comment author: madhatter 26 April 2017 06:07:13AM *  3 points [-]

Suppose it were discovered with a high degree of confidence that insects could suffer a significant amount, and almost all insect lives are worse than not having lived. What (if anything) would/should the response of the EA community be?

Comment author: Thomas 26 April 2017 08:30:25AM 0 points [-]

Every atom shall be used for the computronium, anyway. So there will be no (insect) pain anymore.

We should be very careful what to upload then.

But it's the EA, you are asking for. What their response should be?

I have no idea. I don't see any use for this movement in this context. Or in almost any other context, too.

Comment author: Lumifer 25 April 2017 06:08:23PM *  0 points [-]

infinity doesn't work

Infinity is an abstraction that makes thinking about certain problems easier. It's not a feature of reality (=territory), it's a tool for thinking (=map). As with any tool, there are contexts where it is very helpful; there are contexts where it is inappropriate; and there are contexts where it can be misused.

Without the concept of infinity you'll struggle with even basic geometry (consider a line) and calculus becomes an outright impossibility.

Comment author: Thomas 26 April 2017 06:58:16AM 0 points [-]

Without the concept of infinity you'll struggle with even basic geometry

No matter, no matter. The fact that this concept of infinity sometimes makes our life easier, doesn't make everything right about it. Maybe we should try harder. Going the right path isn't always easy, it can be extremely hard. Perhaps unbelievably hard.

100 years ago, they thought that the self reflection is in the core of paradoxes, like Russell's and related.

I thought long ago, that the infinity has its share here. With Yablo's paradox, this is quite obvious. No self-reflection, but still a paradox. But if the Yablo's list of statements is finite, than the last statement is true (vacuous truth), and - no problemo!

I can't live with an infinite number of (even all finite) sentences. Because those statements may all be "every higher on this list statement is false". But that would imply that the next statement is in fact true. Which means that this statement is false. But all saying the same, that would mean it is true. And so on in a circle.

I see a real paradox here, not a curiosum.

Comment author: gjm 25 April 2017 04:40:30PM *  1 point [-]

That's a nicely unfalsifiable bit of bulverism you've got there. I think I agree that "no rational argument would probably do", but we may not mean the same thing by that.

[EDITED to add: I see no particular problem with the use of infinities in mathematics and never have; back when I was religious, I saw the mathematical notion of infinity as clashing a little with my notion of God -- because in mathematics there is e.g. no all-surpassing maximal infinity -- and I don't recall ever, as theist or as atheist, "loving infinity deeply and strongly" or seeing mathematical notions of infinity as doing anything to create or fill "spiritual emptiness". Of course introspection is unreliable, but it's all I've got :-).]

Comment author: Thomas 25 April 2017 05:30:32PM 0 points [-]

I was always an non-spiritual atheist. (But I am a non-progressive, too,)

It may seems a bit naive, but when I have heard (as a child) about that paradox about omnipotent god who can't create a rock so heavy that even he couldn't lift ... then I suddenly "knew" that quantities too big are (logically) problematic. Let alone infinite quantities.

Today, Yablo's paradox is already good enough for me, to convince me that the infinity doesn't work. How everybody doesn't agree with me about this - baffles me.

Comment author: Thomas 25 April 2017 02:30:26PM 0 points [-]

Can you please substitute "protokol2020" with "Thomas".

It's me in both cases, but here I am better known as "Thomas".

Thank you.

Comment author: gjm 24 April 2017 05:50:39PM 1 point [-]

Ah, that explains a thing or two. You're not trying (or at least not trying very hard) to make what you say make sense because you want it not to make sense, "to discredit", and you don't expect it to make sense because you're using concepts you think don't make sense themselves.

But the actual likely outcome is what's happening here. No one is saying (and I bet no one is thinking) "this doesn't entirely make sense -- obviously the notion of infinity is problematic" but some people are thinking "huh, Thomas seems either confused or unreasonably unwilling to clarify".

If you want to discredit something, the first step is to take it seriously.

Comment author: Thomas 25 April 2017 07:02:19AM 0 points [-]

The not so far away superintelligence will understand. ;-)

I came to the conclusion, that most people love the infinity so deeply and strongly for a reason. Otherwise their spiritual emptiness would be really unbearable. The infinity is a leftover after their abandoned religion, or a pillar of their actual religion.

So, no rational argument would probably do here.

Comment author: Lumifer 24 April 2017 09:09:42PM 0 points [-]

So lessee, who do we tie up and place on trolley tracks?

Comment author: Thomas 24 April 2017 09:26:08PM 0 points [-]

Real life trolley, not an imagined one.

Some people choose to throw 10 instead of 2, since nobody will ever know.

Comment author: Thomas 24 April 2017 08:53:19PM 0 points [-]
Comment author: contravariant 24 April 2017 06:17:45PM 0 points [-]

Evolution is smarter than you.

Could you qualify that statement? If I was given a full time job to find the best way to increase some bacterium's fitness, I'm sure I could study the microbiology necessary and find at least some improvement well before evolution could. Yes, evolution created things that we don't yet understand, but then again, she had a planet's worth of processing power and 7 orders of magnitude more time to do it - and yet we can still see many obvious errors. Evolution has much more processing power than me, sure, but I wouldn't say she is smarter than me. There's nothing evolution created over all its history that humans weren't able to overpower in an eyeblink of a time. Things like lack of foresight and inability to reuse knowledge or exchange it among species, mean that most of this processing power is squandered.

Comment author: Thomas 24 April 2017 08:52:14PM 1 point [-]

Well, we have a race with evolution in the field of antibiotics, don't we? Evolution strikes back with antibiotic resistant bacteria. It is not that obvious that we will win. Probably we will, but that is not guaranteed.

It is a blind force, all right. It has no clear focus, all right. But still, it is an awesome power not to underestimate it.

Comment author: gjm 24 April 2017 01:59:50PM 0 points [-]

So yes, English is computable

I wonder whether we're at cross purposes. I think you're arguing that English is Turing-complete in the sense that you can describe in English any computational process you please; the question I posed was sort of dual to that, namely whether English is computable in the sense that there exists a computer program that perfectly distinguishes valid English sentences from everything else.

I think the boundaries of "valid English sentences" are fuzzy, which already makes that problematic. Otherwise, if we nail down the definition of "English" to something like "agreed by a majority of fluent English-speakers in April 2017 to be valid English" then the answer is probably yes because we can "just" simulate all those fluent English-speakers.

But, again, all that applies only to finite sentences. You want to allow infinitely long "sentences" too, and that opens up a whole lot of other cans of worms.

Comment author: Thomas 24 April 2017 02:12:51PM 0 points [-]

I don't like infinity of any kind. I oppose it strongly, it's a kind of mysticism by my view.

BUT, until it will still be officially permitted in mathematics, I will use it to discredit. To show how problematic it really is.

View more: Next