I am looking for a structure designer app that does the following.
In this app you can enter lists of drawings where each drawing can be entered either by dragging the finger to draw a picture or by selecting pictures from the pictures folder or taking pictures via the camera and perhaps editing them or taking a screenshot. These drawings can be viewed in a scrollable list, vertically, so that there is a first drawing, a second drawing, and so on. Each drawing can be represented by a miniature picture of the drawing which the app computes, or, even, alternatively, by a small Unicode font symbol, or by a small emoticon, which the user selects, and the app associates with the drawing. This, small font symbol or emoticon, can also be drawn (or edited in a pixel based small editor). To each drawing, the user can then record a spelling, which is drawn in calligraphy or in font symbols, and a recording, which records, in an arbitrary pronunciation and made up word, what that drawing is and what the corresponding symbol or miniature picture represents. Thus, even though there is a vertical list of drawings on the first main screen, on the second main screen you can edit the particulars of language and symbolic association for that drawing.
Ok, this is the first part of the app.
These drawings will comprise the letters of a mathematical magma to be listed in a multiplication table or the numbers in some base equal to the number of drawings to be used in a multiplication table of an abstract algebra magma system as described below.
So the second part. The user can define instances of a mathematical operation on the drawings which go forming part of a structure table to be filled out in the third part of the app. For instance,
D1 D2 = D3
Remember, that in abstract algebra, the meaning of an operation is simply here that of a function that assignes to two symbols placed next to each other (here, two drawings), a third symbol (the third drawing). The app must allow the user to view the equation symbol wise or drawing wise.
The kid, who is a genius using the app, can define in this way, several operations, and each operation has its equations. For each operation, you can write down the meaning of the operation, and the meaning of each equation associated with each operation. You can see, the drawings D1, D2, D3. You can see them as drawings, or as symbols, emoticons, symbols.
For example, the first drawing D1 could be of a kid sitting down in school, the second D2 of a kid standing up in school, and since the drawing of the kid sitting down is next to the the one sitting up, the operation could interpret this as the two scenes being next to each other, that is, once kid is sitting, and the next is standing, by each other, in school. The result, the drawing D3 could be the drawing of the teacher's reaction. These can have assigned gibberish sounds given to them. They can have emoticons (if one person smiles, and the other shouts, the third one scorns, for example).
So, many equations can be defined, and pronounced in a custom spoken and written language.
So, each set of drawings, can represent an alphabetical system of letters, or a number system in an abstract algebraic structure.
Now the third part.
The drawings laid out as operations in the second part form part of an addition/multiplication/operation table here. The table, has the symbols, of each drawing, laid out across at the top and down on the left. The (i,j) entry of the table is the result of the operation Di Dj =Dk in the equations (defined, by the user).
The user here can fill out the blanks, or let the system make suggestions based on algebraic structures such as semigroups or groups, if possible, or at all feasible. The most generic structure would be that of a magma (see Wikipedia for mathematical definitions, or see the GAP algebra system to go more deep into the issue, if required, or desired, although this would be a bit too complex, since, the entries of the magma, after all, need not satisfy any particular rules, but the system may notice or deduce some, and point them out).
The user can click on each symbol in the table and view the drawing, along with an explanation of what the drawing is, to remember the meaning of what they are viewing.
Based on each set of equations, and table, if the user chooses to define one in part three, here the user can edit a story, writing it down, based on the equations defined in the second part.
Here, imagination, combining mathematics and literature, gives away.
That is, here the user can further the explanation in text of when they were explaining in the equations and make a story based on the relations, so that it can be pleasant to read and remember everything, based on what happens in the equations.
Thank you for writing this app. I think it would be revolutionary, and really needed. It would, create, a basis, for mathematical applications of algebra, through literature, and allow the user to indulge in memory games where they memorized arbitrary multiplication tables, alphabets, and number systems, if not stories based on these, made up by the user.
It would be a change.
And it would be a start.