Comment author: anonym 25 August 2009 05:23:10AM *  2 points [-]

I looked through a paper of Pearl's to see what causal diagrams look like, and what I saw seemed like a good match for Graphviz. I noticed that Shalizi used it for many of the diagrams in his thesis too.

Comment author: Daniel_Lewis 25 August 2009 01:55:00PM 0 points [-]

Graphviz is the LaTeX of graph-drawing tools. You'll get professional-looking output immediately, but the customization options aren't as discoverable as they would be in a visual editor.

If you plan on making lots of graphs or want them to look very pretty, I'd recommend it. If you're just looking for a quick way to draw a graph or two explaining TDT vs. CDT it may not be worth the time relative to a generic (vector) drawing program.

(The Python bindings might make things marginally easier if you know Python and don't want to learn more syntax.)

In response to Suffering
Comment author: djcb 03 August 2009 05:55:58PM 0 points [-]

Interesting question....

Could there be suffering in anything not considered an MSA? While I can imagine a hypothetical MSA that could not suffer, it's hard to think of a being that suffers yet could not be considered an MSA.

But do we have a good operational definition of 'suffering'? The study with the fish is a start, but is planning really a good criterion?

The discussion reminds of that story On being a bat (iirc) in Hofstadter/Dennets highly recommended The Mind's I, on the impossibility of understanding at all what it is like to be something so different from us.

In response to comment by djcb on Suffering
Comment author: Daniel_Lewis 03 August 2009 08:41:17PM 2 points [-]

The discussion reminds of that story On being a bat (iirc) in Hofstadter/Dennets highly recommended The Mind's I, on the impossibility of understanding at all what it is like to be something so different from us.

Thomas Nagel's "What is it like to be a bat?" [PDF], indeed included in The Mind's I.

In response to comment by dclayh on Pain
Comment author: Alicorn 02 August 2009 07:42:21PM 4 points [-]

But an alternate way to phrase that is that being in pain supplies you with a new, generally overriding goal: to get out of pain. Unless you think that, in general, acquiring new goals is bad, or that, in general, you shouldn't have goals that aren't maximally compatible with each other, I don't see what's necessarily bad about acquiring the goal "get out of pain" - unless you have an independent reason to think that the situation which yields that goal (pain) is bad.

In response to comment by Alicorn on Pain
Comment author: Daniel_Lewis 03 August 2009 01:18:46AM 0 points [-]

I'm not sure quite what you mean by goals here. The most plausible interpretation I can offer is that:

Goals are the drives that cause behavior. "Because of goals X and Y" is an answer to "Why did you do Z?" (and not an answer to "Why should you do Z?").

In this case, we ought to adopt the set of goals that (through the actions they cause) maximize our expected utility. Our utility function needn't mention goal-achievement specifically; goals are just the way it gets implemented. Acquiring a goal uncorrelated with our utility function is bad, because value is fragile.

It's not that the causes of the goal "get out of pain" are bad; it's that the consequences might be. For a wide range of utility functions (most of which make no explicit mention of pain), a system that provided information about damage without otherwise altering the decision-making process would be more useful.

Comment author: JGWeissman 19 May 2009 06:13:01PM 2 points [-]

We could figure out that our symbolic manipulation is inconsistent with the axioms based on the quirk you consider.

There are more axioms needed to define Peano Arithmetic. Taking axioms 7 and 8 from Wikipedia, translated into your notation:

\a. Sa != 0 \ab. Sa = Sb -> a = b

(I also use the symmetry and transitivity of equality.)

Note, from the axioms you stated:

\a. S0 + a = 0 + Sa = Sa

So, axiom 8 can be restated as:

\ab. S0 + a = S0 + b -> a = b

So, starting with your result:

SSS0 = SS0 + SS0 = S0 + SSS0

But also,

S0 + SS0 = SSS0 = S0 + SSS0

So, by the restatement of Axiom 8:

SS0 = SSS0

And then using the original form of Axiom 8 twice:

S0 = SS0 0 = S0

We have a contradiction of Axiom 7.

Thus, it is proven that our symbol manipulation does not follow the Peano Axioms. This does not invalidate the Peano Axioms. It simply means that a given physical system does not follow them. Of course, it would be difficult for people living in an alternate universe where symbols really behaved this way to notice the distinction. And they likely would not have to, if all objects behaved that way; they would figure out some other math to represent their situation. And at some point, mathematicians in their ivory towers would develop this weird math that is really hard to write down and has no known application in the real world (both properties bringing great joy to these academicians).

Comment author: Daniel_Lewis 19 May 2009 07:37:04PM *  3 points [-]

You're right. PA is still consistent (i.e. has a model) even if

 N = the set of strings of the form S*0
0 = the string "0"
S = the function that prepends "S" to its argument

fails to be one because of the way string concatenation works. There's nothing mathematically special about theories that can use physical objects as a model.

(Minor quibble: the definition of addition isn't an axiom. It's just a relation definable in the first-order theory of arithmetic.)

In response to Supernatural Math
Comment author: conchis 19 May 2009 01:15:00PM *  3 points [-]

My (perhaps naive) take on this proceeds from the assumptions that

  1. we can define mathematical operations any way we like (provided we build up consistently from axioms etc.)
  2. the mathematical operations so defined may provide us with more or less useful models of the world.

Parts of this discussion seem to me as though they're conflating these two issues.

We can axiomatize things such that 2+2=4 is, in a particular sense, 'true'. We could do this independently of whether or not it were generally the case that if we took 2 bananas and 2 more bananas and stuck them together we consistently ended up with 4 bananas. If, whenever we took 2 bananas and stuck them together with 2 more bananas, we ended up with 3 bananas, 2+2=4 would still be 'true' in the abstract sense that it proceeds naturally from the axioms, but it would no longer be a useful model to apply to the real world situation of taking-2-bananas-and-then-taking-2-more-bananas-and-sticking-them-together. It would, in that particular sense, be 'false'.

In response to comment by conchis on Supernatural Math
Comment author: Daniel_Lewis 19 May 2009 04:39:20PM *  2 points [-]

If, whenever we took 2 bananas and stuck them together with 2 more bananas, we ended up with 3 bananas, 2+2=4 would still be 'true' in the abstract sense that it proceeds naturally from the axioms[.]

I'm not so sure of that. If putting 2 S's next to 2 S's got us 3 S's, we could prove 2+2=3 in PA with the usual definition of addition:

(dfn) \a. 0 + a = a
(dfn) \ab. Sb + a = b + Sa
\a. SS0 + a = S0 + Sa = 0 + SSa = SSa
SS0 + SS0 = SSS0

Depending on the universe's other rules for putting n things next to m things, we might also be able to derive "2+2=4". In this case, we would decide that PA is inconsistent! Whatever the other rules are, this already shows that the "abstract" conclusions we can draw from a set of axioms depend on the way symbol manipulation works in our world.

I don't think this is really a problem for your argument, but it's an interesting complication. Many (most?) physical facts seem to have no influence on the symbolic manipulations we can use to derive them. For instance, symbolically computing a series for pi doesn't seem to involve any actual circles the way shuffling symbols to add 2 and 2 in PA involves putting SS next to SS.

Powered by Reddit Powered by Reddit