[ExI] Google LaMDA avheives enlightenment
Giovanni Santostasi
gsantostasi at gmail.com
Mon Jan 23 22:45:35 UTC 2023
So not sure what happens, ChatGPT will make these silly math mistakes but
then if you ask to analyze the calculation step by step it realizes its
mistake.
It can also give you code to do the calculation yourself.
I apologize for any confusion in my previous response. The equation 83^3 +
93^3 = 12709775 = 4104 is incorrect.
1.
The first step is to calculate the cubes of 83 and 93, which are: 83^3 =
5292877 93^3 = 7408899
2.
The second step is to add the cubes of 83 and 93, which gives: 5292877 +
7408899 = 12709775
3.
The last step is to compare 12709775 with 4104, which is clearly
incorrect as 12709775 is much greater than 4104.
I apologize for any confusion caused by this mistake, I will double check
my work before providing any math answers in the future. As I mentioned
before, finding the taxicab numbers can be a difficult task and it requires
a lot of computational power, and it's not a trivial task. It is an open
problem in number theory and it's still not known if there is a general
method to find them. Once again, I apologize for any confusion caused by my
previous mistake.
There are several algorithms that have been proposed to find taxicab
numbers more efficiently than a brute force approach. One such algorithm is
the Fermat factorization method. Here is an example of a MatLab code that
implements this method to find taxicab numbers: % Function to find taxicab
numbers using Fermat factorization
function find_taxicab_fermat()
for n = 1:20000
a = ceil(n^(1/3));
b = ceil(n^(2/3));
while (a^3 - b^3)^2 < 4*n^2 && b < 2*a
if (a^3 - b^3)^2 == 4*n^2
fprintf('%d = %d^3 + %d^3\n', n, a, b);
end
a = a + 1;
b = n^(1/3) + (a^2 - n)^(1/3);
end
end
end
% Call the find_taxicab_fermat function
find_taxicab_fermat();
Copy code
% Function to find taxicab numbers using Fermat factorization
function find_taxicab_fermat()
for n = 1:20000
a = ceil(n^(1/3));
b = ceil(n^(2/3));
while (a^3 - b^3)^2 < 4*n^2 && b < 2*a
if (a^3 - b^3)^2 == 4*n^2
fprintf('%d = %d^3 + %d^3\n', n, a, b);
end
a = a + 1;
b = n^(1/3) + (a^2 - n)^(1/3);
end
end
end
% Call the find_taxicab_fermat function
find_taxicab_fermat();
On Mon, Jan 23, 2023 at 2:06 PM Giovanni Santostasi <gsantostasi at gmail.com>
wrote:
> Yes, I agree it is difficult sometime to know if ChatGPT uses its database
> to answer questions or it arrives to the answers using deductive logic.
> It can do logic but you need very careful constructed prompts. I did the 4
> years old theory of mind test and he was able pass it but then it confessed
> that he knew about the test. It is still pretty amazing tech, given it has
> the number of free parameters of a rat brain. I'm intrigued by how well it
> does logic given that it was not trained necessarily to do logical
> reasoning.
> I will probe more its math capabilities.
>
>
> On Mon, Jan 23, 2023 at 2:02 PM spike jones via extropy-chat <
> extropy-chat at lists.extropy.org> wrote:
>
>>
>>
>> *.*> *On Behalf Of *Giovanni Santostasi via extropy-chat
>> *Subject:* Re: [ExI] Google LaMDA avheives enlightenment
>>
>>
>>
>> ChatGPT has no problem with TaxiCab number:
>>
>> The smallest number that can be expressed as the sum of two cubes in
>> three different ways is 1729. It can be expressed as the sum of the cubes
>> of 12 and 1 (12^3 + 1^3 = 1729), as well as the cubes of 9 and 10 (9^3 +
>> 10^3 = 1729), and as the cubes of 1 and 12 (1^3 + 12^3 = 1729). This is
>> known as the "taxicab number" and is the smallest such number that can be
>> expressed in multiple ways…. Giovanni
>>
>>
>>
>> Ja Giovanni but of course there is plenty of online documentation for
>> taxicab numbers because of the famous Ramanujan anecdote.
>>
>> To find a number which we can call triple taxis, we need a little more
>> sophisticated software. I can offer 8 of them, but I urge you to spin up
>> some code or search online for them first.
>>
>> This algorithm I derived can get us arbitrarily many triple taxis in a
>> reasonable time (a few minutes (but the code is too large for the margin of
>> this post.)
>>
>> If no one can find any triple taxis, either by code or by search, I will
>> post the solutions on my blog, Math Geezer, which needs some content.
>>
>> spike
>>
>>
>>
>>
>>
>>
>>
>> _______________________________________________
>> extropy-chat mailing list
>> extropy-chat at lists.extropy.org
>> http://lists.extropy.org/mailman/listinfo.cgi/extropy-chat
>>
>
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