“Formulas that update backwards” is the main idea behind neural networks such as LLMs: the computation network produces a value, the error in this value is computed, and then the error quantity is pushed backward through the network; this relies on the differentiability of the function computed at each node in the network.
Can you enter an RSA key and have it produce two prime numbers?
A random tool like this would be the most entertaining possible way for something like that to be unleashed on the world
My brother once suggested that there are probably bits of code/algorithms that would be world changing if they were released in academic journals, but instead were written by some unknowing programmer in an afternoon for their job coding embedded systems for refrigerators.
This particular example may be unlikely, but it's a very fun idea.
A lot of the time engineers are focussed with solving a problem, to build a working machine/program, while academics just want to publish.
This is also true with patents.
Lots of people working in different fields end up reinventing things that have been known to math for centuries, often in clunky roundabout ways. I imagine some of them figure out things not known to math, but it's far more likely to go the other way.
> Lots of people working in different fields end up reinventing things that have been known to math for centuries
I remember reading, about a year or two ago, about a medical doctor that published a paper rediscovering calculus (I just looked it up, it happened in 1994, there’s been many articles and videos about it)
lmao: https://en.wikipedia.org/wiki/Tai%27s_model
This is such a great story
The first example on the main page has a formula with two variables being updated from changing one value. The immediate question I have is if I change the output, where does the extra degree of freedom come from on the inputs? Does one stay locked in place? Unclear.
I am a huge fan of the concept though. It's been bugging me for years that my spreadsheet doesn't allow editing text fields after filtering and sorting them down to the subset I want. I have to go all the way back to the mess of unsorted input rows to actually edit them.
Does one stay locked in place? Unclear.
What is inputs a,b,c,d,and e are polynomial coefficients? I am hoping to get a fields medal plz respond.
I think it would be good if you could lock one of them.
You can.
The idea is very interesting. As a default strategy you could preserve the ratio of inputs by scaling them to match the scaling of the output, instead of making them equal (for addition). Similarly, for multiplication, you could preserve the ratio of inputs as well, by scaling them by nth root of the scaling factor of the output.
In Excel you have goal seek for this functionality. I believe it does some form of numerical solving of the equation system.
Good for every situation when you need to solve equations!
In the context of using spreadsheets I think about solving simple financial or maybe construction/mechanical design problems where you don’t want to solve it manually or program it and a spreadsheet is a quick and useful interface.
It does not. It perturbates the variables and uses a hill-climbing algorithm.
Could you build an inverse kinematics solver with this? (I recently watched a youtube video of someone iteratively working out the solutions for a robotic arm, by alternating modifying the inputs and the results)
A 2d sketcher with constraints is kind of similar. For example the equation
A = B + C
Where A, B, C are the lengths of 3 parallel lines. Within the sketcher you can drag the length of any one of those lines and the other two will adjust to keep the constraints.
This is really cool! It's like Excel's goal seek but can also handle the case of arbitrary input cells. Goal seeek can only handle one input and one output cell.
But how do you handle the case where multiple variables can be changed? If multiple input cells is the key difference from Goal seek, i think some more rigor should be placed into the algorithm here
e.g. setting A1 + B1 and wanting the result to be 5. Currently it bumps both A1 and B1 equally. What's the thought process behind this?
Yeah. The UI could have a lock icon to set, eg B1 should stay fixed and then only A1 would change.
It supports this. If you type # before a number, like #5, it's made constant.
Wow! See the classic https://en.wikipedia.org/wiki/TK_Solver
and Borland's Eureka solver https://nagodede.github.io/eureka/
A bidirectional formula is also known as an integrity constraint in databases (plus some triggers for restoring the constraint upon updates)!
I think the concept is solid. I’ve only had a few minutes of playing with it, but I have the opinion is that from a UX perspective constants are more common than variables. So perhaps a cell containing a constant should not have a #, but a variable should.
Cool!
Constraint propagation from SICP is a great reference here:
Reminds me of functional logical programming languages like Verse. when you specify the output and ask for the inputs, you get all possible inputs.
Hm? I don't get it.
What's the point of calculating backwards non-invertible operations such as addition? Isn't the result just arbitrary?
I made this mostly as a fun challenge :)
You are right that there is some arbitrariness involved when picking a solution, however it's a bit more subtle than that.
Let's say our problem has N free variables.
Step 1 is finding the subset of R^N that is the solution to the root finding problem. If this subset is a point, we are done (return that point). Note that if there is no solution at all bidicalc should correctly report it.
Step 2 is if the solution subset is not a point. Then there is multiple (maybe even an infinity of) solutions, and picking one is indeed arbitrary.
does the algorithm tries to make minimal changes to the free variables ? If we have 1 + 1 = 2 and change 2 -> 4 then -100000 + 100004 = 4 is also a valid solution. When I tried it it changed it to 2 + 2 so perhaps there is optimization but also a valid optimization can be minimal free variable changes in which case it would be 1+3 = 4 and we update 1 free variable instead of 2. I have no idea which is better just curios how it works. I like the idea very much.
They said this:
> Even a normal spreadsheet is fairly complex beast. But the novel thing about bidicalc is the backwards solver. Mathematically, updating a spreadsheet "backward" is a (potentially underdetermined) root finding problem, because we are trying to find a vector of unknowns such that , where F is the function computed by the cells formulas, and G is the objective value entered in the cell. Note that F is not necessarily a single formula, but the result of composing an upstream graph of cells into a single function.
> The actual root-finding solver is a custom algorithm that I made. It a general purpose algorithm that will find one root of any continuous-almost-everywhere function for which a complete syntactic expression is known. It uses a mix of continuous constraint propagation on interval union arithmetic , directional Newton's method and dichotomic search. It is of course limited by floating point precision and available computation time.
But that really doesn't answer your question. I see no reason why the solver wouldn't decide every time it had a two-variable summation that ADD(X+Y) doesn't reverse to X=-90 and Y=100.
You could add hints as a feature to this. E.g. interest = rate × principle
The user hints principle is preferred fixed so they can see what rate is needed for a givem amount of interest.
Hints could have a precedence order (then prefer to fix earlier terms on an operation on a tie breaker.)
It is for fun. Commercial products do not support this because functions are generally not invertible.
Super cool! Well done. Now take it down and never let Microsoft get their hands on the code, or the entire economic system will go down in flames.
Excellent (sorry accidental pun)
This is a nice exploration.
Very cool!
I'd love to see a version where cells are "torn off" and named as they were in Lotus Improv and one had a "formula pane" where one could see all the formulae for a spreadsheet.
Would it be possible to create this in Python so that it could be a part of pyspread?
you might like https://omrelli.ug/g9/ which is a similar concept but for graphics
I do like g9! It was a strong inspiration for bidicalc actually!
The examples are great and these bidirectional calculators are something that people would love to have in traditional spreadsheets.
So much so that Credit Suisse, which basically was running everything on heavily modded Excel, created a full language whose outputs were Excel spreadsheets capable of doing that. That thing called “paradise” was a total monstrosity but showed how much people wanted this.
That said, you really need a way to set which cells are fixed and which cells are allowed to move if you want to move past basic examples.
Most times you know what you want to do. like => if the user modifies that cell, find a solution for those specific ones.
If you can enter that info, then you have a lot more constrains for your solver and will avoid a lot of edge cases where everything goes to 0, and you can check that the calculation entered is indeed reversible or not, or if it could have multiple solutions, and so on.
interesting. like Excel Solver? or OpenSolver, Gurobi, other optimizers? or different objective?
LOL! Gemini suggested to implement this to me literally yesterday: bidirectional computations. The example was that given a temperature in Celsius and Fahrenheit, modifying either of them should update their counterpart. In angular that would be two linked signals for instance, but even that is a bit fringe. Gemini was going for something even more elaborated.
I told Gemini that spreadsheets were actually not doing that and that I had ways to implement that behavior without the complexity.
Just writing that to show the rabbit hole people are going to fall into if they let their llms go brrr. ;D
In any case, the problem is interesting. The point was to include bi-directionality inside a graph of computations so that we didn't get bogged down by cycles. The benefit being that it would handle float precision issues.
My more manual solution expect that floats precision issues are handled explicitly. I think that this level of explicitness is needed anyway for proper floating point error mitigation.
That's weird, Gemini told me not to do this.
To not do what, to not implement a constraint solver for bidirectional formulas? If you input my above comment it is for sure going to weigh the pros and cons. https://gemini.google.com/share/f40bf53d9c21