Please help me with this math problem.

[yrreg]

I need mathematicians to tell me whether the quotation below makes any sense mathematics-wise; and please explain to me in man-in-the street-language what the author is saying.

 

I am here posting a summary of my proposed technical definition of 'Friendliness'. Readers will need a reasonable background in mathematics and FAI theory for this to make sense because this is only a brief summary. However it should make sense to those with sufficient background knowledge.

 

PROPOSED TECHNICAL DEFINITION OF FRIENDLINESS

 

Marc Geddes, 19th January

 

Explanation of Term: 'Friendliness' is the attribute of 'being ethical'. It is what creators of AGI's want to have in their creations.

 

Propositions: Minds are 'utility functions'. In the limit that the Omega Point condition is approached, our universe could be interpreted as a kind of mind. Therefore all 'concepts' in reality could be interpreted as 'utility functions' in a 'Universal Mind'.

 

Explanation of Terms: The Omega Point condition is the condition that the rate of computation in the universe approached infinity as time approached its boundary (the end of time).

 

It is proposed that 'concepts' be interpreted as utility functions. By this is meant that any concept should be regarded as equivalent to the mathematical function capable of generating a list of all things possessing that attribute, in the limit of the function understood by a super-intelligence at the Omega Point.

 

For example: The concept of 'Beauty' would be defined to be equivalent to the mathematical function capable of generating a list of all beautiful things. This function is uncomputable, since 'beauty' is a prospective attribute: there is no finite function capable of generating or classifying all possible examples of beautiful things. However if we define Beauty to be the function in the limit of that understood by a super-intelligence at the Omega Point, then the definition works, since computation approaches infinity as the Omega Point approaches.

 

Definitions:

 

Concept X=

Function UCX=

Function listing all things with attribute X in the limit understood by a super-intelligence at the Omega Point

(Uncomputable function for prospective attributes)

 

Function PCX=

Finitely specifiable approximation function to the function UCX

(Computable function)

 

 

Propositions: 'Friendliness' is a concept. By the reasoning above, 'Friendliness' is a utility function. Since 'Friendliness' is a prospective attribute , the exact function is uncomputable (since there is no finite function which can generate or classify all possible examples of friendly sentients). Therefore all friendly sentients will have a finitely specified approximation function to friendliness. But truly friendly (ethical) sentients will want to be as friendly as possible. Therefore the approximation function will have the property that it is recursive (self modifying) and converges towards the exact friendliness function in the limit that the number of recursions approaches infinity.

 

Technical definition of Friendliness

 

'Friendliness' is equivalent to the uncomputable utiliy function UCF. Each individual friendly sentient (being computable) is equivalent to a finitely specified approximation function PCF. PCF has to be a function which takes any finitely specified approximation function (PCX) as input and outputs a modified version of that function PCX', such that using successive outputs as the next input causes the output to converge upon UCX as number of recursions approaches infinity. This means:

 

PCF (PCX) =PCX' where PCX' converges towards UCX as number of iterations approaches infinity.

 

Since PCF is itself an approximation function, it modifies itself (uses itself as input into its own function). Then:

 

PCF (PCF) = PCF', where PCF' converges towards UCF as number of iterations approaches infinity.

 

Thanks for any help from anyone skilled in mathematics.

 

yrreg

[Dave]

Doesn't make a lot of sense to me, but I only skim-read it.

[yrreg]

Doesn't make a lot of sense to me' date=' but I only skim-read it.

__________________

Dave

Mathematics Forum Moderator

 

 

Quote:

Originally Posted by KHinfcube22

CAN YOU GUYS STOP SPEAKING EURO ENGLISH AND SAY IN AMERICAN WHAT LOLLY ROFFLES ARE!!! [/quote']

Dear Dave:

 

Can you put in a little bit more attention to my query; so that I would know at least that the citation is saying something mathematics-wise, or is just into mouthing mathematics-looking babble.

 

yrreg

[jordan]

It's an abismal use of mathematics as far as I can understand. From what I gather, he's trying to quantify emotions by using limits and it's just not comprehensive.

[Guest dbj]

This is not a math problem. I think it's a very esoteric point concerning artificial intelligence computer theory. I read something about the "Omega Point" condition in a book by a physicist named Tipler a few years back, and it's waaaay out there. I don't think you'll get much from trying to understand this.

 

Dave

[matt grime]

Anyone heard of Sokal? Just because you can phrase it in pseudomathematical language doesn't make it maths. In fact it appears to be nonsense since there are no references to explain any of the undefined terms.

[Dave]

As I said before, it doesn't make much sense. I've read it a bit more thoroughly, and it still doesn't make any sense at all. I think there's a bit of a consensus on that.

[yrreg]

Thanks, everyone.

 

I am glad to have genuine mathematicians here to help me decide whether some mathematically looking paragraphs are really into mathematics or into some pretentious babbling.

 

Thanks again.

 

yrreg

[matt grime]

You can summarize why it is nonsense quite simply:

 

friendliness is defined in terms of another undefined unmathematical term, being ethical.

 

The first proposition then states that minds are utility functions. A quick check on utility function will show you that is an idiotic pronouncement, mathematically. Nor does the author even propose to show what MAY be reasonable, that decision making processess may be modelled with a utility function.

 

It also continues in that proposition with a series of unrelated deductions without any explanation or evidence.

 

It also contains a very odd statement that any mathematical "function" that assigns "beauty" is uncomputable. This is clearly a dubious statement. The universe contains only a finite number of objects, so assigning a functional value seems eminently computable. It strikes me the author is confusing the philosophical difficulties inherent in defining such a subjective attribute with a mathematical statement that has no such problem.

[bloodhound]

i generally avoid these like a plague