Important Note: I toyed with the idea of calling this product MightyMath for fun. Then my common sense kicked in
and I went back to a name I created in 1979. You will find some references to MightyMath here and there.
They will be eliminated.
T/Maker Five: It's Alive! Email:
not the biggest. It's not the most built-in functions. It's not the
fanciest charts. There was no artist nor writer nor web
designer involved. It's put together without a team or venture capital or focus groups. And no effort was made to follow
Apple, Windows, or Java guidelines for user interfaces. You may never meet anyone that uses it. That said, it's the most
unusual way anybody, anywhere has ever tried to tackle the problem of doing calculations easily and confidently on a
computer. It's a small step up in thinking from a hand caculator, but a giant leap in terms of what you can do. And so, I
gave it life and ask you to give it a try. Here's a home made video to start with.
Is this really necessary? A formula in every cell calculated? It isn't.
T/Maker is an amazing way to MAKE TABLES
and do math without formulae or even cell names.
Calculation trails with "name your own" memories and self-evident syntaxes make math a snap.
upon a time, a long time ago, there was a T/Maker, then a
then a T/Maker 3, and then a T/Master. And now, there is a
T/Maker 5. Is this a fairy tale or a Frankenstein? Try it and be the
judge. You can, BTW, exchange data with most spreadsheets using
character separated values (csv). Thanks for the visit. Peter
Excel for Beginners (video)
Videos: Explanations of most features.
T/Maker is written in java and runs on Mac
/ Apple Computers, Windows,
and a number of other platforms.
Version: There is an "in
progress" version available for download. Feel free to try it at this page link.
can solve a wide range of
problems. You can do simple arithmetic on rows and columns that will
back memories of elementary school. You can do more complicated
calculations in the sequence order style of a hand calculator using
your names for memories and a visual syntax. You can
even do simulations with logical branches and iterations. In all cases,
you will never write a formula that requires a knowledge of
precedence or relies on parentheses (aka, algebra). And you don't
have to learn what you don't need to use. T/Maker is
dedicated to doing your math and tables in a way that is easier,
faster, less obscure, less stressful, and far less mistake prone
than a dreadsheet. Try a Google search of "costly mistakes made with
spreadsheets." Quite incredible!
I believe there is a lot of educational value here. Even elementary
school students could learn to consider and solve a wide variety of
with what you might call "Advanced Arithmetic." Thinking
logically is a more important skill than the label given to the branch
of mathematics one is using.
different screens to do different tasks. The first five buttons on
the toolbar shift between them--data only, calculation trails, formats,
lines, and graphs. With a dedicated screen and handy Assistors, tasks
For everyday math problems, it feels more like a paint program. Hopefully you watched the first video
to get the idea.
T/Maker can be used by most anyone to keep their books, plan
their future, prepare invoices, estimates, or compare alternatives that
into numbers. The overhead of doing calculations is so minimal, it's
worth firing up for a problem involving just a few numbers. It
is not a replacement for use in the business world. That die is cast.
But in your own
world, you may find T/Maker is even fun. It has no hidden
formulae constructed by the program itself. Even some hardened Excel
users will admit that the painting approach, the way calculations are
reused, and the availablitiy of memories you name yourself are
refreshingly "cool" ideas.
probably learned math by starting with addition in elementary school.
From there you progressed to subtraction, multiplication, and, much
harder, division. Along the way you solved problems expressed in this
8 6 12
+2 +9 -3 -8 x 8 x 9
The first pocket-sized
calculators in the seventies, picked up where this approach left off.
A little window showed a current value in the calculator.
add 20, you
could type 20 and push the "plus" button. You could continue with more
values and more operators and more intermediate results to your heart's
content. There was never a formula. This is a close model to the way
T/Maker works. If you look at the
"Simple Arithmetic" example
you will see that putting a plus sign next to data cells adds the
adjacent value to T/Maker's calculator.
All spreadsheets give cells a name based on their column/row
intersection and require a formula using those
names. Parentheses are used in the standard approach to control the
order of operations. That formula is put in the
cell where you want the result to be. A
formula of B1 + B2 would be put in B3 for the simple example, and the
screen would show the
value 7 instead of the formula.
The truth be told, you could have put "+B1+B2=" in
cell B3 in T/Maker. You could also have put "+B1+B2=B3" in cell Q45 and
job done. But why bother with that? T/Maker lets you accomplish
calculations in the most
simple, obvious way without rejecting other possibilities.
In T/Maker, the
calculation requested may often be written in elementary school,
as well as little windows for the values (like everybody
else), T/Maker has little windows for the calculations as
well. Your calculations are not hidden. Nor do they become a mystery
for you solve a few days later.
Suppose you wanted to do this same simple arithmetic across three
columns to include neighboring fruit stands. A spreadsheet can
the initial formula with a shortcut, so it can generate more hidden
formulae to do a similar calculation in other locations. Thus cell C3
the formula C1 + C2 and cell D3 would get the formula D1 + D2.
And both new formulae would be replaced by the values they calculate.
T/Maker offers a different approach. You get a darkened square
cursor and simply click it on the places where you want to restart the
same series of calculations anywhere in the table. What I
like about T/Maker is that this screen represents my problem in
the way I conceived it. Nothing is lost or added or confused by a
is an example, much later, where nearly 100 made-up formulae in a
spreadsheet are eliminated, and that's on just eight rows .
Some quick terminology: The above calculation is called a trail. A
trail is composed of a series of ordered steps.
Each step can
have one or many operations to perform. They are numbered as you enter
them, but you can change the order if necessary. Some trails are
vertical or horizontal, but the steps in a trail can wander all over
the place. A
single trail can produce many results in different cells incorporating
many operations and equal signs. It is not a formula which has a
lifespan of only one equal sign.
One of the nice things that came along with hand calculators was a
button with an "M" on it. That stood for "memory." In essence, it
you a sort of second little window that you could not see. You could
put a value into that window and fetch it back as needed. It was great
for at least one intermediate result. Well, you can do the same thing
in T/Maker, but you can pick your own name (with a few limitations),
and you can have as many as you want.
Some syntax notes: A step in a trail, for the most part, contains a
series of operators followed by an associated value (or NOT).
For example. "/6"
is in an instruction to divide the value in the calculator by 6, that's
the value associated
with the division sign. When
an operator has no associated value, it is interpreted
to reference the value to its right in the white data cell. Consider
"+ /5 *9 +32". The plus sign has no associated value, so that is an
instruction to pluck the value from the cell, add it to the calculator
(assume zero for now), divide by 5, multiply by 9, and add 32. If the
value in the cell were a temperature in centigrade, the value in
calculator would now be the Fahrenheit equivalent.
Memories (in terms of syntax) are just associated values
constants in the previous paragraph except they can also be used after
an equal sign to store a value in them. You cannot put a constant
after an equals sign or it wouldn't be very constant. Here's the
example used on
the green board above:
say I wanted to calculate the cost per square inch of something
circular from its diameter. Here's
this solution: row 1 holds the diameter and step 1 calculates the area
from it. Put the diameter in the calculator with the + (no associated value
here), /2 to get
the radius, ^2 to
*pi to multiply by pi (a
built-in memory), and =area
to put the result in the memory
named "area." Step 2 puts the cost in the calculator, and step 3
divides it by the area and outputs the value to the cell (no associated
help keep things simple and straightforward. And a memory name you
more intuitive than a raw cell name. This trail uses no cell
names which makes it an excellent template that can be
reused with a click of the mouse starting from other locations. No need
for more hidden formulas.
Along with constants and memories, you will sometimes find a single
letter used as the associated valued for an operator. Most
spreadsheets and tables have rows that derive values for a row from
data on that
row. The single letter refers to the column on the row where the
is being used. Here's our Per Inch example
turned in another direction. I purposely put all the activity on a row
that has no numbers and did the whole calculation in one step. It's not
the way I would usually do this, but it highlights the utility of this
The associated values that represent the values in the columns are
single, capitalized here, letters which are the column names. I did put
the area in a memory
"sq". Notice the step is defined on the row of headings, but only
used on rows 2, 3, and 4. All this looks like it ought to be illegal,
but it isn't. T/Maker doesn't eliminate options for its own
convenience. This also forms a template that is easy to reuse on other
rows without any ambiguity.
Let's summarize, the bread and butter "associated values" that
you should know. Remember, no associated value means the adjacent cell.
1) Constants: 12.5, 91650
2) Memories: area, sq, profit, gross, you name them.
3) Row relative columns: C, g, E
4) Specific cells: Q21, b18 (not recommended for templates to be
reused, they create confusion)
Clearly, T/Maker does not view your problem as nothing more than
a matrix of pigeonholes. Some tasks are. But most are not. T/Maker
allows you to take advantage of the structure you have in a
remarkably intuitive way. This separation between the calculation
itself and where it is used is unique, I believe, to T/Maker.
Reusing a calculation by clicking at another starting spot is about as
it can get. And your intentions are clear to T/Maker and will be clear
to you the next time you revisit your table.
Some screens and explanations:
you saw in the video, T/Maker
has different screens to do different tasks that you can move through
calculating trails screen has
two cells for each column as do the formats and graph screens. One
holds the symbols. The other holds
the data which can
be edited on the screen as well. The top of the first screen below
Lite Assistor for trails from which symbols can be fetched as a cursor
into place or more complicated commands can be built. You can also edit
the green cells directly. There is a demo video on using this Assistor
and its bigger brother on the videos page. (Link at top of
This table presumably
belongs to a new car owner who wants to track his
MPG. There are three trails shown below. Maybe a minute of work. You
probably wouldn't have to write them all, but the a spreadsheet would
have 9 hidden formulae for this simple job.
BTW, I would refer to the approach below as the "click and paint"
solution. No keystroke is required to do it.
it came to adding a new row, you could select the last row above the
total, choose Insert Cloned Row(s) from the Row/Col menu, and enter
data. These trails would all be updated correctly as would formats,
lines, and even any graphs you might have specified. There is
also a video of Cloning that uses the example of calculating means,
standard deviations, and a correlation coefficient between two
variables. Tough stuff can be done.
Below is the
more weighty version of this Assistor. You
can calculate a mortgage payment with six clicks. One on "mpy" to start
the cycle, one on a cell with the amount, one on a cell with the
interest rate, one on a cell with the years, and one on the cell where
you want the result. Then one on the Compute button. A similar approach is
used to calculate present value and growth rates. You
will not, however, find the full variety of built-in functions of a
long established spreadsheet. It's not that you cannot calculate
anything, it's just
that you have to solve it yourself (at least for now).
can have multiple steps in a trail associated with the same cell.
When you click to edit a
green cell that already has one or more steps,
you will get a choice for what to do. When editing a green cell, you
can edit the step's symbols and/or
its number if you want to change the order of steps.
can also work from a list of all steps in a trail which is an easy way
to review your trail in sequential order or modify a step with no
questions asked. Just
select the step and push the button of interest. The screen will be
adjusted to show the correct step if you want to edit it.
After a quick look at the other dedicated screens, there is a section
at the end showing solutions to more challenging problems and a great
tool that helps you find mistakes--the Debugger. I am hesitant to
overwhelm anyone with solutions to problems that are beyond those they
expect to encounter.
Setting formats is easy. There is an Assistor to create new
ones, but most of
the time you can get one directly from the formats toolbar. Get the
cursor for it and paint it into the secondary cells (blue for formats).
You can even
select an area of cells and fill the whole area with a single click.
The Assistor is shown in the screen below.
Decorative lines can make a table more understandable and
when you print it. You probably already have an idea how that might
look. Again, you can paint with a cursor and/or fill areas. The screen
is below. There are no symbol cells because you can see what's in place
without them. You
can also show these lines on the data screen if you have developed some
sort of app for others to use.
And then there are graphs which I probably should have called
What do you do? As expected! You get a cursor or fill an area with
symbols that represent the content of those cells. Here L's are for
labels and V's are for values. About 30 seconds of work. And there
are always defaults for text elements, so you can just mark values to
start with. Some charts allow up to three series of values so there are
V1, V2, and V3 cursors. Actually
there are bunch more cursors. It all depends on the type of chart you
are making. When you click on the graph type, the parameter box will
fill with the appropriate ones. If you change the chart and have
already specified values, T/Maker will try to adapt the values of
one chart to a different type. It's pretty good at that, but some
situations are impossible--what to do with an X-axis on a pie chart for
Here's the pie chart for the above effort. The graphs, like
built-in functions, are more limited than in a long established
they can provide insight or help make a point like any others. And you
can call them up from the data screen where you might be discussing
some numbers that support your conclusion. This
is a package I obtained from JFreeChart (very grateful for that). Once
the image is up, options are controlled by that package and offered
with a right mouse click. I have to admit, I have not studied them.
is the print box for tables (not graphs) which tells you how many pages
wide and pages long the output will be. You can reset the parameters
that affect the size and recalculate. If you are just interested in
keeping historical paper records, you can save paper and ink this way. You
can make some nice forms too--not that I want to contribute to the
number of forms in the world though I would like more space to actually
write the address! Here's a (scanned) invoice
printed with some lines. New rows could be added by cloning so work
could be done on the data screen only with additional rows cloned.
There may be a person here or there who is interested in the
ability to do simulations like the roulette example later. There might
be a few more interested in the other example that saves a hundred
formulae on a some business style rows. Everyone should probably take a
glance at the Debugger screen. It's a great tool for finding mistakes.
The major leap here is the way calculations are performed and
represented on the screen. The ease of use across the various screens
is nice as well. It can be used be youngsters (pre-algebra) and adults
they "don't do math." The price will probably be around $5 to purchase
at this site. I wonder about and would like to pursue
relationships with school districts. I believe T/Maker has
There is a "work in progress" demo version now that is missing
some features, but appears to be solid across all basic functions. Your
a welcome to pass a link to any and all.
More Complicated Features And Problems
something is likely to lead to a typo or requires you to
remember a keyword or a special syntax, there is typically assistance
available. Here is the Assistor for a "when clause" which allows you to
perform calculations or take various actions based on a logical
test. It's not hard to make one, but why not get
it right the first time while seeing what the options are? The number of possible
combinations is in the hundreds.
As one example,
you could put a
category in a column and use certain trails only on certain
All trails, nonetheless, could be marked to apply to every row but
would only do their thing on rows which are the correct category. Thus
rows of any
category could be inserted anywhere and would be correctly calculated
without requiring any modifications to any trail. In the
below EXTRAIL is short for "exit trail." All the following steps in the
would be skipped for, say, an "adult." "<>" stands for not
equal. Think of it as less than or greater than, so therefore not
equal. Other comparisons are self-explanatory.
when text <> "child" extrail
I thought we
should take a look at something that might seem to be a bit more
business oriented. Below is such a thing with various derived rows from
two rows of data. Almost 100 numbers are derived which would be almost
one hundred cells with formulae regardless of who wrote them or how.
Well, there are two trails in T/Maker for the almost 100 derivations.
Let's take a look at the first one which calculates the cumulative and
monthly average to date for both years. The exclamation point ( ! )
value into the calculator. A plus sign (+) actually adds the value. If
ended last step with an equal sign (=), the calculator would already be
zero, but if you really are starting from scratch, the ! is the
preferred choice. The hash sign (#) outputs the value in the calculator
but does not set the calculator back to zero. Sometimes you want to
output values and pass them on. Sometimes you don't.
The first step below enters the value in column B (no associated
value), adds the value in memory csum (initially zero), and puts that
total in the csum memory. This trail is reused first across the twelve
columns of 2018 before it is used across the 12 columns of 2019. As we
go though the columns, we have csum up to date for the column we are
on. The order in which the trails are reapplied is always left to
right within top to bottom. For the average to date, I will need
know what to divide csum by. In the second step, I have put the
cumulative in the correct spot first (= has no associated value). Then
I have used another
"! count + 1 = count" to count columns for the divisor needed to
get the average to date. The third step does the division and outputs
When I first computed this table the second set of numbers were
far too high. The problem was easy enough to find. The memories
csum and count started off with the values left over from the first
of rows. Thus I added a fourth step to set csum and count back to
zero after the 12th month was calculated. The second trail is below.
The second trail calculated the monthly increase and percent
increase. That was a snap. I did have to visit cell B2 twice. Once to
subtract it from cell C2 to get the raw increase and once to divide the
increase by B2 to get
the proportional increase. A multiplication by 100 got me the percent.
The bright green square, BTW, is an indicator
that the cell has multiple steps. You can also see that in the helpful
list of all the steps discussed earlier. T/Maker tries to keep all
related information in your face and not hidden.
When there is a problem, like the one I had, it's typically in a
area and takes a tweak to fix. You will soon see a debugging tool that
is a great feature in T/Maker. In summary the above two screens in
conjunction with the darkened green
cells do the work of nearly 100 formulae in a spreadsheet.
And if you plan to do 2020 and 2021, it will be closer to 200 formulas.
take a look at a table which simulates the optimal strategy for
roulette and demonstrates that T/Maker is ready to rise to most any
level you want to go to. In this example, you enter what you
want to risk, how much you want to make, and a
maximum number of spins. T/Maker will bet on your lucky number every
time with a dollar amount that achieves your goal on the first win. The
more you risk and the less you want, you can win much more often than
not. Of course, when you do lose, it's a bummer. Note below that
direct references are made to individual cells like B7 or B4. The
trails here are for one task only and not needed as templates. Also,
you can see the cells involved are all on the same screen, so a mistake
is much less likely. The particular
trail below sizes the bet which is put in a memory as there is no cell
for it. "Cel" in step 4 stands for "ceiling" which is the
first integer bigger than the number in the calculator. You can't bet
a half chip. Nor can you bet more than you have left--step 5.
wonder if spreadsheets could even do this sort of thing? This
table is not child's play, but I believe most everyone could look
through the trails and understand how it works. Others can solve
similar problems or even more complicated ones. It
does restart itself after each spin until you're broke, won the desired
amount, or played the maximum number of spins specified. A variety of
such options were shown on the weighty Assistor under the heading "Flow
you put various restarts in a table and it goes on for more than
15 seconds, T/Maker will give you the opportunity to abort with
some restart statistics shown. This can happen if you never get to an
And when you do
most anything, it's nice to have a way to find
mistakes. T/Maker has a debugger that can walk through calculations,
trail by trail, step by step, even operator by operator. It shows
pretty much everything about this moment in this table including
recent references made to other cells and memories. At this point in
the above example, 13
bets have been lost. We're down $136 and betting $12 a spin. That would
get us to our target profit of $300, but the bet will go up if we
continue to lose. It's fun to take a table and walk through it
even if it is working correctly.
am going to mention one more "expert" feature that shines in some rare
situations. If you end a memory name with a question mark (qfactor?),
question mark is replaced by the column in which it is used. This means
you can have a single trail used down all columns with a "= qfactor?"
and have a "! qfactor?" to fetch the correct value for that
way down the table in a completely different trail.
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