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From: Christopher Maloney <dude.domain.name.hidden>

Date: Thu, 03 Jun 1999 22:23:27 -0400

As I mentioned in my last email, I'm new to this list. So if

this topic has already been discussed, I apologize.

The argument I want to make is related to the "Doomsday

argument" that I just read on one of your websites (I can't

remember whose). In that argument, one draws conclusions

about one's environment based on the proposition that the

SAS that you are is likely to be an "average" one. That is,

each of us can assume that we are a sort of random sample

among all possible SAS's of similar complexity. That's

the most general form of the statement that I would feel

comfortable making.

It seems plausible that our complexity, or our information-

processing capability, is not an accident. If it were much

less, we would probably not be self-aware. I don't know

why it's not much more than it is, although I (of course)

have a theory about that too.

Anyway, Tegmark, in his paper, made some rather extravagant

claims, IMO, that:

It appears likely that the most basic mathematical

structures that we humans have uncovered to date are

the somae as those that other SASs would find.

He attempted to justify this idea using anthropic reasoning,

which I found awfully dubious. I just don't have the

confidence that he expresses that we humans aren't "missing

something" when it comes to the types of mathematical

structures possible. I would guess that the field of

mathematics just keeps getting more varied, more bizarre,

and more rich, the more it is studied. How could we possibly

know that there aren't more SAS-supporting structures of types

that we cannot yet dream?

On the other hand, I believe that one can reason that the

environment we find ourselves in must be as it is, or at least

must be typical, using the concept that each of us is a

typical SAS.

It's very simple: if the measure of the infinite number of

SAS's allowed by one mathematical structure A is greater than

that in structure B, then we *must* find ourselves A or in

yet another structure with an even greater measure. That is,

we must find ourselves in the structure which admits the

largest number of SAS's of our complexity.

This idea first occured to me when pondering the vast number

of branches allowed by MWI QM. I haven't investigated this

fully, but I think it's of the order of 2^c, where c is the

cardinality of the real numbers. I could be wrong. Anyway,

it's big.

The logical continuation of this idea is that the order of

SAS's allowed in our mathematical structure must be utterly

unbounded. I don't know how to describe this, perhaps

Aleph-infinity. Isn't it true that for any infinite cardinal

number, there is another that is of a higher order? I'm a

little rusty on this - I have to re-read my primer on

infinities. But I just wanted to get this idea out, so my

terminology might be screwed up.

But how could the cardinality of the allowable SAS's in our

mathematical structure be "utterly unbounded". The only way

that I can conceive of this is that the laws of physics

are an infinitely deep well of complexity. That, for example,

when we find a theory of quantum gravity, that it allows for

yet a higher order of SAS's than that allowed by the standard

model. But then we would find that that is still not the

ultimate theory, and when we dig further, we find yet more

possibilities. I can't see any aesthetic reason for assuming

that the "structure" we are in would ever be completely well

demarcated to us, in our frog perspective.

Thoughts?

Date: Thu, 03 Jun 1999 22:23:27 -0400

As I mentioned in my last email, I'm new to this list. So if

this topic has already been discussed, I apologize.

The argument I want to make is related to the "Doomsday

argument" that I just read on one of your websites (I can't

remember whose). In that argument, one draws conclusions

about one's environment based on the proposition that the

SAS that you are is likely to be an "average" one. That is,

each of us can assume that we are a sort of random sample

among all possible SAS's of similar complexity. That's

the most general form of the statement that I would feel

comfortable making.

It seems plausible that our complexity, or our information-

processing capability, is not an accident. If it were much

less, we would probably not be self-aware. I don't know

why it's not much more than it is, although I (of course)

have a theory about that too.

Anyway, Tegmark, in his paper, made some rather extravagant

claims, IMO, that:

It appears likely that the most basic mathematical

structures that we humans have uncovered to date are

the somae as those that other SASs would find.

He attempted to justify this idea using anthropic reasoning,

which I found awfully dubious. I just don't have the

confidence that he expresses that we humans aren't "missing

something" when it comes to the types of mathematical

structures possible. I would guess that the field of

mathematics just keeps getting more varied, more bizarre,

and more rich, the more it is studied. How could we possibly

know that there aren't more SAS-supporting structures of types

that we cannot yet dream?

On the other hand, I believe that one can reason that the

environment we find ourselves in must be as it is, or at least

must be typical, using the concept that each of us is a

typical SAS.

It's very simple: if the measure of the infinite number of

SAS's allowed by one mathematical structure A is greater than

that in structure B, then we *must* find ourselves A or in

yet another structure with an even greater measure. That is,

we must find ourselves in the structure which admits the

largest number of SAS's of our complexity.

This idea first occured to me when pondering the vast number

of branches allowed by MWI QM. I haven't investigated this

fully, but I think it's of the order of 2^c, where c is the

cardinality of the real numbers. I could be wrong. Anyway,

it's big.

The logical continuation of this idea is that the order of

SAS's allowed in our mathematical structure must be utterly

unbounded. I don't know how to describe this, perhaps

Aleph-infinity. Isn't it true that for any infinite cardinal

number, there is another that is of a higher order? I'm a

little rusty on this - I have to re-read my primer on

infinities. But I just wanted to get this idea out, so my

terminology might be screwed up.

But how could the cardinality of the allowable SAS's in our

mathematical structure be "utterly unbounded". The only way

that I can conceive of this is that the laws of physics

are an infinitely deep well of complexity. That, for example,

when we find a theory of quantum gravity, that it allows for

yet a higher order of SAS's than that allowed by the standard

model. But then we would find that that is still not the

ultimate theory, and when we dig further, we find yet more

possibilities. I can't see any aesthetic reason for assuming

that the "structure" we are in would ever be completely well

demarcated to us, in our frog perspective.

Thoughts?

-- Chris Maloney http://www.chrismaloney.com "Knowledge is good" -- Emil FaberReceived on Thu Jun 03 1999 - 19:42:50 PDT

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