I think the interesting question is what does the function on natural 
numbers

      n → shortestDescriptionOf(n)/n

look like.

- pt

On Friday, March 1, 2019 at 3:22:59 PM UTC-6, Lawrence Crowell wrote:
>
> There are numbers that have no description in a practical sense. The 
> numbers 10^{10^{10^{10}}} and 10^{10^{10^{10^{10}}}} have a vast number of 
> numbers that have no description with any information theoretic sense. This 
> is even if all the particles in the some 10^{500}cosmologies in the 
> multiverse or with 12-dimensions some 10^{10100} cosmos's were employed as 
> information bits. It is also not hard to construct a Berry paradox for a 
> vast number of numbers here. 
>
> LC
>
> On Monday, February 25, 2019 at 1:35:49 PM UTC-6, Philip Thrift wrote:
>>
>> via
>> https://twitter.com/JDHamkins/status/1100090709527408640
>>
>> Joel David Hamkins   @JDHamkins
>>
>> *Must there be numbers we cannot describe or define? Definability in 
>> mathematics and the Math Tea argument*
>> Pure Mathematics Research Seminar at the University of East Anglia in 
>> Norwich on Monday, 25 February, 2019.
>>
>>
>> Abstract:
>>
>> *An old argument, heard perhaps at a good math tea, proceeds: “there must 
>> be some real numbers that we can neither describe nor define, since there 
>> are uncountably many real numbers, but only countably many definitions.” 
>> Does it withstand scrutiny? In this talk, I will discuss the phenomenon of 
>> pointwise definable structures in mathematics, structures in which every 
>> object has a property that only it exhibits. A mathematical structure is 
>> Leibnizian, in contrast, if any pair of distinct objects in it exhibit 
>> different properties. Is there a Leibnizian structure with no definable 
>> elements? Must indiscernible elements in a mathematical structure be 
>> automorphic images of one another? We shall discuss many elementary yet 
>> interesting examples, eventually working up to the proof that every 
>> countable model of set theory has a pointwise definable extension, in which 
>> every mathematical object is definable.*
>>
>>
>> http://jdh.hamkins.org/must-there-be-number-we-cannot-define-norwich-february-2019/
>>
>> Lecture notes:
>>
>> http://jdh.hamkins.org/wp-content/uploads/2019/02/Must-every-number-be-definable_-Norwich-Feb-2019.pdf
>>
>>
>> - pt
>>
>

-- 
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.

Reply via email to