1/15/2026 - Is Pseudocode Abstract or Concrete?

While reading Selected Papers on Computer Science by Don Knuth, I was struck with a realization. His explanation of an algorithm versus a program complements what should be taught in computer science classrooms. First, write the algorithm, then write the program. As he says, one algorithm may have many programs. To me that seems to make it harder to write the program first. You must not only come up with the algorithm, but the implementation (of many which are possible) as well.

"To me the word algorithm denotes an abstract method for computing some output from some input, while a program is an embodiment of a computational method in some language. I can write several different programs for the same algorithm [...]."

He continues on to say

"[...] I don't know any way to define any particular algorithm except in a programming language."

Source: amazon.com

This statement surprised me. Maybe it is because of the strict definition of "an abstract method for computing" that is holding this definition of an algorithm back from a more general algorithm. Even so, would simply writing down steps to an algorithm in English suffice? Where does pseudocode fit into all of this. Does it count because its like a programming language? Well it's also very much like English too! If we broaden computing to doing some operation, could a recipe for chocolate chip cookies be an algorithm?

I think it makes sense to think of an algorithm thorugh a narrow lens and to study and look at algorithms in a computer science or mathematics sense. Although, maybe the recipes and the English steps are how we can program our brain!

I think Knuth may argue that all of my examples are still embodiments of an algorithm, just more abstract or ambigious than a programming lanugage. How does that fit into the idea of writing the algorithm first, then programming it? Well, if the psuedocode I wrote is now considered a program, will I ever be able to represent the algorithm without some approximate representation? This is diving into a more philosophical problem of an abstract idea and its concrete representation (Philosophy Now, "Plato: A Theory of Forms").

The concept of 2 is represented by the number 2. It can also be represented by II or two (and many more). Even 10 in binary. It's hard to distinguish the concept from the representation. After further introspection, I may agree with Knuth on this point more than I had thought. So when we teach students to come up with an "algorithm" first, we may really mean to represent the algorithm in a higher-level sort of "program" (psuedocode), as to allow for ambiguity that will be removed when a more concrete "program" is written (C, C++, Python, Java). Even the set of steps we may call and algorithm, with some input and output, is really an abstract-like "program."

All this is to say, I was both surprised and intrigued by Knuth's definition. It took me from a concrete understanding to a not-so-concrete understanding, to Plato and forms, and back to a more practical way of thinking of "algorithms."

Selected Papers on Computer Science, "Algorithms, Programs, and Computer Science" Donald E. Knuth, 1996.

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1/15/2026 - Conway's Surreal Number System

Recently, I watched a YouTube video about Surreal Numbers and the book written by Don Knuth (called Surreal Numbers), about a number system created by John Conway. After watching the video I was intrigued, so I went to the University Library and found a copy.

YouTube: Surreal Numbers (writing the first book) - Numberphile

The book can be hard to follow and I often times would need to write down examples to follow, but it was really fun going through it. It is written as a dialogue between Alice and Bill, two people who end up on an island and find a rock explaining an ancient number system. It explores their journey in uncovering this system similar to a mathematician discovering a new field of math, as Conway may have.

While I eventually bought my own copy, a copy can be found in a library or as a PDF online. Here is an excerpt about the rules of these surreal numbers, as found written on an ancient tablet. Note the humorous name change of John H. Conway as John H. W. H. Conway, in reference to the Hebrew name of god.

"In the beginning, everything was void, and J. H. W. H. Conway began to create numbers. Conway said, "Let there be two rules which bring forth all numbers large and small. This shall be the first rule: Every number corresponds to two sets of previously created numbers, such that no member of the left set is greater than or equal to any member of the right set. And the second rule shall be this: One number is less than or equal to another number if and only if no member of the first number's left set is greater than or equal to the second number, and no member of the second number's right set is less than or equal to the first number." And Conway examined these two rules he had made, and behold! They were very good. And the first number was created from the void left set and the void right set. Conway called this number "zero," and said that it shall be a sign to separate positive numbers from negative numbers. Conway proved that zero was less than or equal to zero, and he saw that it was good. And the evening and the morning were the day of zero. On the next day, two more numbers were created, one with zero as its left set and one with zero as its right set. And Conway called the former number "one," and the latter he called "minus one." And he proved that minus one is less than but not equal to zero and zero is less than but not equal to one. And the evening ..."

Source: amazon.com

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1/14/2026 - A Computer "Bug"

A computer "bug," which is an actual moth, likely found by a member of Grace Hopper's team in the 1940's. As well the term referring to a bug as a mechanical defect was already in use, specifically by Thomas Edison.

https://americanhistory.si.edu/collections/object/nmah_334663

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1/14/2026 - Grace Hopper's Compiler

Here is a good article I found while surfing the web titled "From Punch Cards to Python" which exlpores the history of Grace Hopper's A-0 compiler.

https://spectrum.ieee.org/from-punch-cards-to-python

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1/14/2026 - GoTo Jail, Do Not Pass Go!

Ever wonder why GoTo went the way of the Dodo in high-level programming? Well, Edsger Dijkstra wrote a short paper in 1968 giving a great explanation of GoTo's faults using the concepts of mental load and textual and dynamic indices.

Go To Statement Considered Harmful, Communications of the ACM Volume 11, Issue 3

Source: geeksforgeeks

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