On Wed, Aug 22, 2018 at 4:43 PM <agrayson2...@gmail.com> wrote:
>
>
> On Tuesday, August 21, 2018 at 3:22:04 PM UTC, Jason wrote:
>>
>>
>>
>> On Tue, Aug 21, 2018 at 1:16 AM <agrays...@gmail.com> wrote:
>>
>>> I've been looking at the Wiki article on this topic. I find that I
>>> really don't understand what it is, or why it's important. Maybe a few
>>> succinct words from the usual suspects can be of help. TIA.
>>>
>>>
>>>
>>
>> Bruno provided a great definition and background of the Church-Turing
>> Thesis. I will try to answer why it is important and comes up often in our
>> discussion.
>>
>>
>> The Church-Turing thesis says that anything that is computable is
>> computable by any computer. In other words, there is nothing that the
>> computer in your cell phone can't compute, that your laptop or that a super
>> computer (or even a quantum computer) can. It just comes down to having
>> enough time and memory.
>>
>> This is why you don't need to buy a new phone with new hardware every
>> time you want to install a new app. Regardless of the type of CPU in your
>> phone, it can be extended in its power of what it might compute only given
>> some new software. It is in this sense that computers are "Universal",
>> they are universal in the same sense that of a universal remote, or in the
>> sense that a record player is a universal sound imitating device. A record
>> player might emulate the sounds of an orchestra, Britney Spears, whale
>> songs, etc., all it needs is the appropriate record and it can produce the
>> sound.
>>
>> In the same sense, all a Turing Machine (computer) needs to imitate (or
>> emulate) the right program or function is the right software. Because of
>> this, anything that can be described in software, be it a brain emulation,
>> an AI, a virtual environment, a virtual machine or operating system, can
>> never know what hardware is running it, because the Church-Turing thesis
>> says that any computer is capable of running it.
>>
>> This is why if consciousness is computable (the computational theory of
>> mind) we cannot know what is computing us (e.g. we could be in a matrix
>> type simulation for all we know). The other implication is that if
>> computations exist in mathematics (and they do), then we exist within
>> mathematics. Mathematics (or at least the part necessary to describe
>> computations) becomes the fundamental science of what we experience and
>> what is possible to experience or what we may predict about our future
>> experiences (physics).
>>
>>
>> Jason
>>
>
> If someone digitizes (emulates) the Mona Lisa, is this equivalent to the
> Mona Lisa?
>
If you digitize a person and put the digitized Mona Lisa before them, it is
equivalent to the real Mona Lisa to that person, at least as far as they
can tell.
> Can you write a function which is not computable? AG
>
>
>
If by not computable you mean it never returns, then this is easy:
function foo():
while (true)
{
// loop forever
}
There are also programs for which no one knows if they are computable or
not. If you can prove whether or not this function ever completes, you
will be world famous, and may even earn a million dollars (though I think
the prize has been retracted, it might be oferred again):
Step 1: Set X = 4
Step 2: Set R = 0
Step 3: For each Y from 1 to X, if both Y and (X – Y) are prime, set R = 1
Step 4: If R = 1, Set X = X + 2 and go to Step 2
Step 5: If R = 0, print X and halt
All you have to prove is the computer either never gets to step 5 or that
it does get to step 5. Mathematicians have been working on a related
problem for 300 years, no one has solved it yet.
Jason
--
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.
