Strange math syntax in old basic listing

Question

I'm browsing through an old book "Basic Computer Simulation" from 1983. It contains a line of BASIC code that reads:

LET Z1 = M * D1 * (PQ / A) [ 3

I understand all of the code except the "[ 3" I don't ever remember that syntax in any BASIC I learned.

The book calls it a "universal subset of BASIC" and says it has been tested on a TRS-80 Model III. Similar lines of code appear in other listings in the book so I don't think it is just a typesetting error.

Another formula in a different listing is:

LET H = H1 - .5 * G * (T1 - T) [ 2

This is a formula for a falling object.

Answer 1

Your mention of TRS-80 provides a clue. In the TRS-80 character set, the space normally occupied by the ASCII [ character is instead a ↑ (up arrow) character. Old versions of BASIC (such as this one from 1964) use the up arrow character to indicate exponentiation, probably because at that time the ^ character was not even in the ASCII standard. (There is another question on this site Why do we use caret (^) as the symbol for ctrl/control? which addresses the evolution of ^.)

Your second example LET H = H1 - .5 * G * (T1 - T) [ 2 provides another clue, as it is a formula for position of a falling object, which has a square in the time term.

So, in this book, the [ character represents the ↑ up arrow character because [ in ASCII occupies character number 91, the same as ↑ in the TRS-80 character set. (Note that this differs from the original 1963 ASCII, where ↑ was character number 94.)

When the book was typeset, there may have been a character set conversion problem where this discrepancy was not noticed, or for some reason the publisher simply could not print the ↑ character.

Answer 2

In old computer books of cheaper sort, (Paperback or pocket books) it was quite common that they couldn't type set all special characters directly. Either they did as in this case, changed the character for something the computer in question didn't use, but the type setter could handle. In this case this is normally mentioned in the foreword of the book. Otherwise you had someone add the character manually to the text. I've seen both versions, even in official manuals...

In this case the [ was a substitute for arrow up, or "to the power of". This is clear from the second example in the question.

Answer 3

It is the exponentiation operator.

Why is that?

On a TRS-80 Model III the line of BASIC entered would literally be:

LET Z1 = M * D1 * (PQ / A) [ 3

To get the [ character you would press the up arrow key.

You would press the same up arrow key on its predecessor, the TRS-80 Model I. However, it would display as:

LET Z1 = M * D1 * (PQ / A) ↑ 3

This is because the Model I's character set had a few differences from ASCII. Where ASCII has the [ \ ] ^ characters the Model I has ↑ ↓ ← →.

You might wonder why the Model III didn't use ^ for exponentiation. The main reason is that it would prevent compatibility with the Model I which was a big feature of the Model III (even though there were some incompatibilities). I suppose it is possible that the Model III could have accepted both [ and ^ for exponentiation but then those Model III BASIC programs wouldn't be backwards compatible with the Model I.

I also speculate that Tandy would not have been comfortable making the change to the BASIC ROM themselves and would not have been interested in paying Microsoft to do it.