Wiki Contributions


Your account of "proof" is not actually an alternative to the "proofs are social constructs" description, since these are addressing two different aspects of proof. You have focused on the standard mathematical model of proofs, but there is a separate sociological account of how professional mathematicians prove things.

Here is an example of the latter from Thurston's "On Proof and Progress in Mathematics."

When I started as a graduate student at Berkeley, I had trouble imagining how I could “prove” a new and interesting mathematical theorem. I didn’t really understand what a “proof” was.

By going to seminars, reading papers, and talking to other graduate students, I gradually began to catch on. Within any field, there are certain theorems and certain techniques that are generally known and generally accepted. When you write a paper, you refer to these without proof. You look at other papers in the field, and you see what facts they quote without proof, and what they cite in their bibliography. You learn from other people some idea of the proofs. Then you’re free to quote the same theorem and cite the same citations. You don’t necessarily have to read the full papers or books that are in your bibliography. Many of the things that are generally known are things for which there may be no known written source. As long as people in the field are comfortable that the idea works, it doesn’t need to have a formal written source.

At first I was highly suspicious of this process. I would doubt whether a certain idea was really established. But I found that I could ask people, and they could produce explanations and proofs, or else refer me to other people or to written sources that would give explanations and proofs. There were published theorems that were generally known to be false, or where the proofs were generally known to be incomplete. Mathematical knowledge and understanding were embedded in the minds and in the social fabric of the community of people thinking about a particular topic. This knowledge was supported by written documents, but the written documents were not really primary.

I think this pattern varies quite a bit from field to field. I was interested in geometric areas of mathematics, where it is often pretty hard to have a document that reflects well the way people actually think. In more algebraic or symbolic fields, this is not necessarily so, and I have the impression that in some areas documents are much closer to carrying the life of the field. But in any field, there is a strong social standard of validity and truth. ...

I agree on most of this, but would you mind explaining why you think neuroscience is "mostly useless?" My intuition is the opposite. Also agreed that pure mathematics seems useful.

Would you mind tabooing the word "preference" and re-writing this post? It's not clear to me that the research cited in your "crash course" post actually supports what you seem to be claiming here.

If you can come up with better images to represent Friendly AI, please let me know!

How about an image of a paper clip?

Apologies for the pedantry that follows.

Today, we know how Hebb's mechanism works at the molecular level.

This quote gives the impression that there is a unitary learning mechanism at work in the brain called "Hebbian learning," and that how it works is well understood. It is my understanding that this is not accurate.

For example, spike-timing-dependent plasticity is a Hebbian learning rule which has been postulated to underlie at least some forms of long-term potentiation and long-term depression. However, there is ongoing debate as to how accurate/useful this concept is, including one recent attempt at a re-formulation of classical STDP.

With regard to molecular mechanisms, it was my understanding that even fundamental issues like whether LTP/LTD primarily involve presynaptic or postsynaptic modifications (or both) have not yet been cleared up.

I think your statement should be changed to something like "Though there are likely a variety of Hebbian learning mechanisms at work in the brain, neuroscientists are beginning to understand the few of them that have been discovered so far."

That thread is way too long, so I'm not going to read it, but I did a quick search for and didn't see any discussion on what I consider the dealbreaker when considering the evidence for or against most religions (but especially any flavor of Christianity), which is the existence of "souls." Simply put, the "soul" hypothesis doesn't jive with current evidence from physics, and it doesn't pay rent with regard to observations from neuroscience (or any kind of observations, for that matter). I strongly suspect that the Book of Mormon doesn't deal with evidence from neuroscience, which means that, due to the "soul" hypothesis being fairly central to Christian belief (it is the postulated mechanism by which a person is judged for "sins" committed in their life), you don't have to read it.

As an aside, I consider this line of reasoning to be something like "atheism for dummies" since most religions that I've seen depend on humans having something like a soul.

Isn't 12.0 something like quadruple-beta of the "Stable" version of Chrome?

I'm not entirely sure what you mean here. It's the current stable release

OP: For the record, I'm on Chrome 13 and I haven't noticed anything like you mentioned here. The graphical glitches make me think something is up with your video card or the drivers for it, but if it's only happening for LW...I'm not sure what to tell you.

In the past year I've been involved in two major projects at SIAI. Steve Rayhawk and I were asked to review existing AGI literature and produce estimates of development timelines for AGI.

You seem to suggest that this work is incomplete, but I'm curious: is this available anywhere or is it still a work in-progress? I would be very interested in reading this, even if its incomplete. I would even be interested in just seeing a bibliography.

I'm interested in ... winning arguments ...

Ack, that won't do. It is generally detrimental to be overly concerned with winning arguments. Aside from that, though, welcome to LW!

Load More