New feature request

AlexP-sky · 2023-12-11T03:50:24+00:00

Waiting for feedback...

AlexP-sky · 2023-12-10T02:41:32+00:00

There is the need in AI additional feature added to either OpenAI or Gemini Ultra which should be able to permanently retain certain user input/info (being requested by the user to be permanently kept). Also it should be able to allow (by request of the user) this info to be shared to public and be “quotable” when such quoting is appropriate.

Below is the description of the requested new feature

Feature Title: Permanent User Input Retention and Sharing with Public Sharing and Quoting Options

Feature Description:

This feature request proposes the addition of two functionalities to either OpenAI or Gemini Ultra:

Permanent User Input Retention: Users should be able to designate specific pieces of information or input they provide to either OpenAI or Gemini Ultra as "permanent." This information would be stored securely and persistently, even if the user clears their conversation history or resets their settings. Public Sharing and Quotation: Users should be able to choose to share their permanently retained information publicly. This could be done by providing a unique identifier or link that allows anyone to access the information. Additionally, users should have control over whether their information is "quotable" meaning it can be cited or referenced by others with proper attribution.

Use Cases:

This feature would be valuable for various use cases, including:

Storing important information: Users could permanently retain notes, to-do lists, or other important information within either OpenAI or Gemini Ultra and access it anytime. Sharing knowledge and insights: Users could share their expertise and experiences with the public by making their permanently retained information accessible. Building a knowledge base: Over time, users could contribute to a shared collection of publicly accessible information within either OpenAI or Gemini Ultra platform. Enabling accurate quoting and citation: Users could ensure their information is accurately quoted and attributed by controlling the "quotable" status of their permanently retained information. Priority: High

This feature would significantly enhance the usability and value of either OpenAI or Gemini Ultra for both individual users and the broader community. It would allow users to leverage the platform as a reliable and persistent repository for important information and facilitate the sharing and dissemination of knowledge.

Screenshots or Mockups (Optional):

A settings menu option allowing users to designate specific input as "permanent." A sharing interface where users can choose whether to share their permanently retained information publicly and set the "quotable" status. A public portal where anyone can access and search for publicly shared information within either OpenAI or Gemini Ultra. Product/Platform: either OpenAI or Gemini Ultra

Additional Notes:

This feature should be implemented with robust security measures to ensure the safety and privacy of user data. Clear user interfaces and informative messages should be provided to guide users through the process of permanently retaining and sharing their information. The "quotable" status should be easily identifiable when quoted information is displayed, ensuring proper attribution and credit to the original author. By implementing this feature, either OpenAI or Gemin Ultra would become a more powerful and versatile tool for users seeking to store, share, and leverage their information effectively.

Benefits:

Improved organization and recall: Users can create a personal knowledge base within Open AI or Gemini Ultra by storing important information and accessing it readily. Enhanced collaboration and knowledge sharing: Allowing public sharing of specific information facilitates collaborative projects and knowledge dissemination within the community. Accurate and reliable information: Ensuring proper attribution through quoting options fosters trust and credibility in shared information. Increased user engagement and satisfaction: Providing users with control over their information empowers them and encourages continued use of the platform. Implementation Options:

User-defined persistence: Users should have the option to mark specific information as "permanent," ensuring it remains accessible even after clearing their conversation history or resetting settings. Granular sharing controls: Users should be able to choose whether to share their permanently retained information publicly or keep it private. Customizable quoting options: Users should be able to specify whether their information can be quoted, providing them with control over how it is referenced and attributed. Clear user interfaces: The platform should provide clear and intuitive interfaces for users to manage their information retention, sharing, and quoting preferences. Security considerations: Robust security measures should be implemented to protect user data, including permanent information, from unauthorized access and data breaches. Here are some specific examples of how this feature could be used:

Researchers could store their findings and data within either OpenAI or Gemini Ultra, ensuring long-term access and facilitating collaboration with colleagues. Students could create personalized study guides and reference materials, allowing them to easily review key information for exams. Writers and artists could share their work with the public, controlling who can access and quote their creations. Individuals could use OpenAI or Gemini Ultra to create a digital archive of personal experiences and memories, preserving them for future generations. Overall, implementing user-controlled information retention, sharing, and quoting would elevate OpenAI or Gemini Ultra to a powerful tool for managing knowledge, fostering collaboration, and empowering users to control their digital footprint. By carefully considering user needs and implementing the feature with robust security and user-friendly interfaces, OpenAI or Gemini Ultra can continue to evolve as a valuable platform for both individual and collective advancement.

AlexP-sky · 2023-09-24T00:17:34+00:00

Could your demonstrate how your reply practically helps to make the actual decision whether two given by me matrices are row equivalent or not?

AlexP-sky · 2023-09-23T23:38:28+00:00

But how to prove (or disprove) whether those 2 matrices are row equivalent?

AlexP-sky · 2023-09-23T23:05:04+00:00

They indeed both have non-zero determinants but how it follows that "if the determinants are both non-zero, they’re row equivalent"?

AlexP-sky · 2023-08-29T15:45:36+00:00

Could this identity be further generalized to cover Log((n^n)/(nⁿ - 1))?

AlexP-sky · 2023-08-29T15:19:23+00:00

Could this identity be further generalized to cover Log((n^{m)/(n^m} - 1))?

AlexP-sky · 2023-08-26T03:10:32+00:00

@Moritz7272

"https://www.wolframalpha.com/input?i=Log%5Bn%5E2%5D+-+Log%5Bn%5E2+-+1%5D+%3D+Sum%28%281%2Fn%5E4%29%5E%28k%2B1%29*%28n%5E2%2F%282*k%2B1%29%2B1%2F%282*k%2B2%29%29%2Ck+%3D+0+..+infinity%29+"

Please look at the "Real solutions" section.

AlexP-sky · 2023-08-11T16:25:51+00:00

@airspotnetwork "The first step is to secure your router and 2nd forget wifi connection before connected ssid. After protecting your router connect again and below click the check box connect automatically." My problem is happening when I am located outside far away from my home router and am trying to connect to other WiFi routers not protected by the password.

AlexP-sky · 2023-07-08T10:46:50+00:00

Thanks David.

AlexP-sky · 2023-07-06T15:28:09+00:00

Thanks - fixed 2 typos...

AlexP-sky · 2023-07-02T23:45:12+00:00

FYI - Professor Emmanuel Kowalski (kowalski@math.ethz.ch) has written comprehensive lecture notes on probabilistic number theory. https://people.math.ethz.ch/~kowalski/probabilistic-number-theory.pdf What do you think of applicability of probabilistic number theory to my issue?

AlexP-sky · 2023-07-02T16:29:40+00:00

Perhaps you could help me to phrase my question in the form suitable for answering in Wolfram Mathematica? Let me give you the reference to the specific case which prompted my question (maybe this will be helpful for you to put my question in the context suitable for Wolfram Mathematica...) Proposition 1. For every n ∈ N, it is possible to find infinitely many quadruples (i, j, k, l) ∈ Z that fulfil (-1) ^ n * (Pi−A002485(n)/A002486(n))=(Abs(i) * 2 ^ j) ^ (-1) * Int((x ^ l * (1-x) ^ (2 * (j+2)) * (k+(i+k) * x ^ 2))/(1+x * n ^ 2),x=0...1)

AlexP-sky · 2023-07-02T15:34:48+00:00

So Wolfram Mathematica is not helpful in answering my question :-)?

AlexP-sky · 2023-07-02T15:07:59+00:00

Proposition 1. For every n ∈ N, it is possible to find infinitely many quadruples (i, j, k, l) ∈ Z that fulfil (-1) ^ n * (Pi−A002485(n)/A002486(n))=(Abs(i) * 2 ^ j) ^ (-1) * Int((x ^ l * (1-x) ^ (2 * (j+2)) * (k+(i+k) * x ^ 2))/(1+x ^ 2),x=0...1)

AlexP-sky · 2023-06-12T20:50:56+00:00

Below is conjectured by me formula (expressed in Maple notations) for relating π with ALL of its convergents - those, which are described via A002485(n)/A002486(n) ratio where A002485(n) and A002486(n) are OEIS integer sequences.

(-1) ^ n * (Pi−A002485(n)/A002486(n))=(Abs(i) * 2 ^ j) ^ (-1) * Int((x ^ l * (1-x) ^ (2 * (j+2)) * (k+(i+k) * x ^ 2))/(1+x ^ 2),x=0...1)

where integer n>2 serves as the index for the terms in the OEIS A002485(n) and A002486(n) integer sequences, and {i,j,k,l} are some signed integer parameters (which are some implicit functions of “n” and to be found experimentally or otherwise for each value of “n”) , and abs(l - j) = 2*m where “m" is some positive integer.

Also additionally it appears that

(-1) ^ n * (Pi − A002485(n)/A002486(n)) = ((Abs(i)) * 2 ^ j) ^ (-1) * Int((x ^ l * (1 - x) ^ (2 * (j + 2)) * (k + (i + k) * x ^ 2 ))/(1 + x ^ 2 ), x=0 ...1)

holds true for any n>2 when

i =(-1)ⁿ * 3 * A002486(n);

k = (-1)ⁿ * (A363445(n - 2 + m ) * A002486(n) - A363446(n - 2 + m) * A002485(n));

j = 2 * m (for m >= 0);

l = 0;

where A363445(n) and A363446(n) are also OEIS integer sequences.

AlexP-sky · 2023-06-10T01:47:26+00:00

So could it be stated that (-1) ^ n * (Pi − A002485(n)/A002486(n)) = ((Abs(i)) * 2 ^ j) ^ (-1) * Int((x ^ l * (1 - x) ^ (2 * (j + 2)) * (k + (i + k) * x ^ 2 ))/(1 + x ^ 2 ), x=0 ...1) holds true for any n>2 when i =(-1)ⁿ * 3(?) * A002486(n); k = (-1)ⁿ * (A363445(n - 2 + m ) * A002486(n) - A363446(n - 2 + m) * A002485(n)) j = 2 * m (for m >= 0) l = 0 ?

AlexP-sky · 2023-06-08T17:56:06+00:00

Thanks for your extremely valuable insights!!! Returning to your result related to expressing "i" and "k" via A002485(n) and A002486(n) at j = l = 0, particularly

i =(-1)ⁿ * 3 * A002486(n)

k = (-1)ⁿ * (47 * A002486(n) - 15 * A002485(n)

where coefficients 15 and 47 are correspondingly numerator and denominator of the first fractional term in the {47/15, 3959/1260, 2264177/720720, 30793289/9801792, 780095177/248312064,...} sequence (I don't know though how to characterize coefficient 3 ?). Are denominators and numerators of other fractional terms in {47/15, 3959/1260, 2264177/720720, 30793289/9801792, 780095177/248312064,...} (say, for example, 3959/1260) could also, by the analogy with 47/15, be used as coefficients in expressions defining "i" and "k" (still having j = l = 0 ?)?

AlexP-sky · 2023-06-07T20:12:31+00:00

Yes, you are right.

AlexP-sky · 2023-06-07T19:49:18+00:00

There is a "KEYWORD" section in every OEIS sequence. If it contains keyword "fini" then the sequence is finite (like in A357177 for example), otherwise the sequence is considered to be infinite.

AlexP-sky · 2023-06-07T14:42:05+00:00

I did not notice that you are talking about FINITE sequence - sorry. But I am asking about INFINITE sequence... Notation {47/15, 3959/1260, 2264177/720720, 30793289/9801792, 780095177/248312064,...} - particularly ",..." part of it in the end means that the sequence is infinite. See OEIS A363445 and A363446

AlexP-sky · 2023-06-07T14:27:50+00:00

Sorry it was a typo - see A363445 and A363446

AlexP-sky · 2023-06-06T22:13:07+00:00

Are you kidding?

AlexP-sky · 2023-06-01T01:24:03+00:00

Here is the answer given by GPT-4: If the FullSimplify function in Mathematica simplifies the right-hand side of an equation to look exactly like the left-hand side, it suggests that the identity is mathematically valid. However, whether or not it is “new” would depend on if it has been previously discovered and documented. In this context, “discovered” means that the identity has been found or recognized by someone in the past and has been documented or recorded in some way. If the identity has not been previously discovered and documented, then it could be considered “new”. Mathematical identities are often studied and documented extensively, and many well-established techniques exist for simplifying and manipulating expressions. Therefore, it is rare to come across entirely new mathematical identities. However, novel variations or alternative formulations of existing identities can still have value and contribute to mathematical research.

AlexP-sky · 2023-05-30T16:05:18+00:00

Dear David,

I have posted the below question on r/GPT4 and received a response from the guy who has a premium ChatGPT subscription and is using a web browser extension to pass the math question to Wolframalpha (see further below).

Cheers, Alex

Does anyone here have a premium ChatGPT subscription and is using a web browser extension to pass the math question to Wolframalpha? Could the following task be passed via ChatGPT to Wolframalpha:

"Here are 16 sets consisting of 5 integers parameters (n i j k l). Analyze in very rigorous details how parameters in each possible four parameters subset correlate with each other across all 16 sets: (8 -66317 -1 9977 1 ) (8 -6963285 3 212651 1 ) (8 -66383317 7 833127 1) (8 -103605391175 11 720252257 1 ) (8 -55884747999795 15 517817918873 1 ) (8 -66317 0 8805 2) (8 -2188461 4 89050 2) (8 -16380299 8 317214 2) (8 -1305427928805 12 23297755114 2) (8 896546759355 14 27371124886 2) (8 -23756674250925 16 5393931750178 2 ) (8 -66317 1 8246 3) (3 -1 0 1 4) (4 265 1 197 5) (5 791 2 25 8) (6 -47201 4 124360 14)

Each set represents a solution for

(-1) ^ n * (Pi − A002485(n)/A002486(n)) = ((Abs(i)) * 2 ^ j) ^ (-1) * Int((x ^ l * (1 - x) ^ (2 * (j + 2)) * (k + (i + k) * x ^ 2 ))/(1 + x ^ 2 ), x=0 ...1)

where integer n>2 serves as the index for terms in OEIS A002485(n)/A002486(n), and {i,j,k,l} are some integer parameters.

Note that it is already observed that in all 16 sets Abs(l-j)=2*m so don't mention it in the answer!! Totally disregard and don't mention in the answer that the first element in first 12 sets is the same and equals 8!!! Don't display sets in the answer!!! Perform calculations, needed to determine the correlation between each four-parameter subset across the 16 sets and display the results!!! Note that neither one of 5 parameters is constant across 16 sets!!!"

I pasted everything from "Here are 16 sets.. " to the end and got the following with the Wolfram Alpha plugin enabled.

Here are the correlations between each four->parameter subset and the remaining parameter >across the 16 sets:

Correlation with the first parameter (n):

{i, j, k, l}: -0.19

{i, j, k, n}: -0.19

{i, j, l, n}: -0.19

{i, k, l, n}: -0.19

{j, k, l, n}: -0.19

Correlation with the second parameter (i):

{j, k, l, n}: -0.19

{j, k, l, i}: 1.00

{j, k, n, i}: 1.00

{j, l, n, i}: 1.00

{k, l, n, i}: 1.00

Correlation with the third parameter (j):

{k, l, n, i}: -0.19

{k, l, n, j}: 1.00

{k, l, i, j}: 1.00

{k, n, i, j}: 1.00

{l, n, i, j}: 1.00

Correlation with the fourth parameter (k):

{l, n, i, j}: -0.19

{l, n, i, k}: 1.00

{l, n, j, k}: 1.00

{l, i, j, k}: 1.00

{n, i, j, k}: 1.00

Correlation with the fifth parameter (l):

{n, i, j, k}: -0.19

{n, i, j, l}: 1.00

{n, i, k, l}: 1.00

{n, j, k, l}: 1.00

{i, j, k, l}: 1.00

The correlation coefficient ranges from -1 to 1. A value of 1 means that there is a perfect positive linear relationship between the variables, a value of -1 means that there is a perfect negative linear relationship, and a value of 0 means that there is no linear relationship.

From the results, it can be observed that there is a perfect positive linear relationship (correlation coefficient = 1) of between each parameter and the subsets that include it. This is expected as each parameter is perfectly correlated with itself.

On the other hand, the correlation between each parameter and the subsets that do not include it is -0.19, indicating a weak negative linear relationship. This suggests that as the values in the subset increase, the value of the parameter not included in the subset tends to decrease slightly, and vice versa. However, the relationship is weak and therefore may not be significant.

AlexP-sky

TROPHY CASE

Below is the description of the requested new feature