Re: Another challenge for the conventionalists: the monster group

['Brent Meeker' via Everything List]

On 9/13/2020 9:45 AM, Bruno Marchal wrote:

Hello,

Some have defended conventionalism in mathematics. I shown that hard 
to sustain in recursion/computability theory, and thus arithmetic. 
Here something which shows that it is hard to maintain conventionalism 
in the study of finite symmetries.


Groups (mainly set of symmetries) can be decomposed into some 
composition of “prime groups” (called simple group).


Who is the guy who decided that a all finite simple groups belong to 
either 18 infinite families of groups, except for 26 exceptional one, 
the sporadic groups, which does not, and who decided conventionally 
that the biggest one is Monstruously big, the Monster, which has



  808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000

elements.

All groups can be represented by a group of matrices, with the 
coefficients belonging to some field (usually the complex numbers), 
with the usual product of matrice. A field is itself a special sort of 
double group. (Not to confuse with quantum field, of filed of forces).
The minimal dimension needed for that representation is the dimension 
of the group. It is dimension of the space in which the element of the 
group represent the symmetries.


The Monster group has dimension 196,883 with the matrix coefficient 
taken in the field of complex numbers, but it has dimension 196.882 on 
the field z_2 with two elements {0, 1}.



Who decided that the dimension of the monster group is 196.882. Divine 
convention? Could a God makes this in another way?


It might play some role in physics, notably conformal fields, 
strings,… (cf Munshine).


A rather nice video on the Monster group is:

https://www.youtube.com/watch?v=mH0oCDa74tE


As I have explained, the non algorithmic distribution of the codes of 
the total computable function is enough kicking back for me to be 
realist on arithmetic, but the Monster group presents, I think, some 
difficulties for the conventionalist too.


Are you claiming someone had to decide on these numbers?  The whole 
point of mathematics is that these are logical implications of axioms, 
and the axioms are quite simple and easily thought of.  So if the axioms 
are conventions and the rules of inference are conventions, then 
conventionalism is true.  Of course one could argue that axioms and 
rules of inference are not arbitrary conventions...they are grounded in 
biological evolution.


Brent

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Another challenge for the conventionalists: the monster group

[Bruno Marchal]

Hello,

Some have defended conventionalism in mathematics. I shown that hard to sustain 
in recursion/computability theory, and thus arithmetic. Here something which 
shows that it is hard to maintain conventionalism in the study of finite 
symmetries.

Groups (mainly set of symmetries) can be decomposed into some composition of 
“prime groups” (called simple group).

Who is the guy who decided that a all finite simple groups belong to either 18 
infinite families of groups, except for 26 exceptional one, the sporadic 
groups, which does not, and who decided conventionally that the biggest one is 
Monstruously big, the Monster, which has

808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000
elements.

All groups can be represented by a group of matrices, with the coefficients 
belonging to some field (usually the complex numbers), with the usual product 
of matrice. A field is itself a special sort of double group. (Not to confuse 
with quantum field, of filed of forces).
The minimal dimension needed for that representation is the dimension of the 
group. It is dimension of the space in which the element of the group represent 
the symmetries. 

The Monster group has dimension 196,883 with the matrix coefficient taken in 
the field of complex numbers, but it has dimension 196.882 on the field z_2 
with two elements {0, 1}.


Who decided that the dimension of the monster group is 196.882. Divine 
convention? Could a God makes this in another way?

It might play some role in physics, notably conformal fields, strings,… (cf 
Munshine).

A rather nice video on the Monster group is:

https://www.youtube.com/watch?v=mH0oCDa74tE 



As I have explained, the non algorithmic distribution of the codes of the total 
computable function is enough kicking back for me to be realist on arithmetic, 
but the Monster group presents, I think, some difficulties for the 
conventionalist too.

Bruno


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Underground QC

[Bruno Marchal]

Hello,

Background radiation and quasi-particles decohere superconducting quantum 
computing device, suggesting to make them working underground!


https://news.mit.edu/2020/cosmic-rays-limit-quantum-computing-0826?fbclid=IwAR0q7rAwj-FRRm3wzDW9HSOYyeH8IXQzOA5RtzTu_0q4o-oJDQ-xew_LLqo
 



In my opinion, and I bet John Clark will agree on this, it is one more reason 
to invest in quantum topological computation. But this, technically, has its 
own big problem to solve.

Bruno

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Re: Probability in Everettian QM

[Bruno Marchal]

> On 13 Sep 2020, at 01:21, PGC  wrote:
> 
> 
> 
> On Thursday, September 10, 2020 at 11:43:48 AM UTC+2 Bruno Marchal wrote:
>> On 9 Sep 2020, at 16:29, PGC > > wrote:
>> 
>> 
>> 
>> On Wednesday, September 9, 2020 at 11:38:32 AM UTC+2, Bruno Marchal wrote:
>> 
>> With Mechanism, we do have an ontological reductionism: only numbers exist, 
>> with only two simple laws: addition and multiplication. Then the physical 
>> reality emerges as a first person plural persistent sharable interfering web 
>> of histories, which is confirmed by quantum mechanics without collapse, up 
>> to now.
>> 
>> It is the believer in a “physical reality out there” to explain how it 
>> manage to make some computations more real than other. It is up to them to 
>> show some evidence for that belief.
>> 
>> That's easy. For millennia, by the rules of your discourse, every 
>> person/number killing another with some weapon essentially states: "This 
>> computation is more real. This one." 
>> 
>> There's been too much evidence of that kind, and any form of determinism 
>> essentially justifies all of that evidence, citing some truth or realism á 
>> la "that's the way the dovetailer runs" in a fatalistic manner. This sort of 
>> relativism leads to forgone conclusions about the nature of life, 
>> essentially disintegrating any/all forms of violence, when science should 
>> pursue said nature of life with the hope of its optimization. I see this as 
>> evidence of ideology within your discourse, as "no ethics" with regards to 
>> numbers is mere nihilism/relativity/fatalism.
> 
> 
> On the contrary, with mechanism there are some objective moral laws derivable 
> from the machine theology, like “it is immoral tp do the moral to the others”.
> 
> That statement tends toward relativism though as it “does the moral to the 
> others” by declaring itself.

Yes. It is a version of Epimenides. Like when I say that the best path to God 
is running away from anyone suggesting a best path to God. It is a remind to 
not take this literally, and then the consistency of such statement is brought 
back by taking the difference between the modes seriously (like between G and 
G*). You are saved from the paradox by not inferring that “it is immoral to do 
moral” as true, but not assertable, especially not as an imperative 
injonction...



> 
> 
> Then mechanism also refute all reductionist conception of humans, as it is 
> refute all reduction conception of machine.
> 
> Many ideologies with gods and their creations offer the same and many go far 
> beyond that. For example, I just now created an ideology of citrus that 
> refutes all reductionist conceptions of everything and offers loyal disciples 
> some vitamin C in any cocktail of their choice. 
> 
> In the cocktail glass we can observe the buoyancy of citrus, so while you 
> guys sit around here wondering about preludes to a metaphysics unstated, 
> drowning in a sea of details and linguistic hallucinations, yours truly and 
> the god of this new ideology that is the oldest ideology remain buoyant.
>  
> 
> 
> 
>> 
>> Even if physics were obtained in a satisfying manner from self-reference, 
>> I'd tend towards interpretations that don't evaporate questions of violence, 
>> good, and evil for some relativism; as tricky as they may be... my hunch is 
>> that those questions related to the large variety of descriptions of 
>> selfhood/subject need further elaboration. 
> 
> 
> The consequence of Mechanism, like of Darwinism, should not be changed 
> according to our wishes. That would be like hiding truth, or a possible 
> truth, for terrestrial purpose. We can build some ethics, but not let it 
> decide for true and false. That was the main error brought by the 
> institutionalisation of religion, I think.
> 
> That assumes absolute truth discerning ability, especially the first two 
> sentences. THAT IS the very error of which the last sentence warns readers.
>  
> 
> 
> 
>>  
>> This requires to abandon digital mechanism eventually.
>> 
>> If you or anyone have still a problem with this, I can explain more. This is 
>> known since the 1930s, but ignored by many.
>> 
>> Bruno
>> 
>> PS I will certainly say more on this, but now I have hundred of exam copies 
>> to note...
>> 
>> You have exam papers to grade now at the beginning of the school year?
> 
> Yes. The second session of September, and the admission exams. Covid-19 
> doubles the work. But it is OK, it is my job.
>  
> Just give admission to everybody!

There are 120 demands, but in this technical school, the pedagogical equipment 
require no more than 10 people per class.
I would like to admit anyone, and even more not to select them through math, 
but I have not much choice in this matter.



> WTF Bruno, why do you complain that folks don’t get into computer science 
> enough but fail them for some exercise failure based on a reductionist 
> conception of humans/machines? The ones you fail will tend to move towards 
> beliefs