lambda

Announcements

• Welcome to IDS-101-13: Thinking Machines!
• Opening Days: Day 3... Do you know where to procure?
  • Over-the-counter medication
  • Prescription medication
  • A COVID vaccine
  • Specialty foods, like electrolyte or meal-replacers
• How did the Pythagorean Triples homework go?
  • Some parts were intended to be obnoxious.
  • I hope you were rigorous around
    • Text formatting
    • Recording your thoughts
    • Collaborating
  • Mostly because it's good practice.
• Today's lecture loosely adapted from here but in a nonobvious way so maybe stay away from that link for now.

Python

• This semester we will use Python
• Python is a language, but a novel kind of language.
  • Python is free,
  • Python is very widely used,
  • Python is flexible,
  • Python is relatively easy to learn,
  • and Python is quite powerful.
• It may be the case that Python can be thought of as the language in which a machine may think.
  • Deliberately weak claim.

Pythogoras

• Let's review the homework
  • If I were you I would:
    • Leave my original homework unaltered.
    • Append anything you learn today to the end.
    • Thereby preserve a record you can look back on.
  • Some elements of the homework were "deliberately annoying"
    • We want to introduce "problems" or even just annoyances before we introduce their solutions.
    • This is supported by some educational literature - you'll just have to let me know what you think.

Review:

• Homework 1 Pythagorean Triples
  • Write code to define positive integers a, b, and c of your own choosing.
  • A few solutions.
    • Multi-line, multi-cell.
      • Create 3 "Code" blocks.
      • Assign one variable in each. a = 3
b = 4
c = 5
        
      • A good way to make quick changes to individual variables.
      • Cell structure is more complicated.

Review:

• Homework 1 Pythagorean Triples
  • Write code to define positive integers a, b, and c of your own choosing.
  • A few solutions.
    • Multi-line, single-cell.
      • Create 1 "Code" block.
      • Make three lines, one variable in each. a = 3 b = 4 c = 5
        
      • A good way to use fewer cells.
      • Individual cells are more complex.
      • This is the Gemini (AI) solution.

Review:

• Homework 1 Pythagorean Triples
  • Write code to define positive integers a, b, and c of your own choosing.
  • A few solutions.
    • Single-line
      • I haven't shown you this, but I when dealing with a "triple" I like to assign it all at once.
      • I use commas to assign 3 variable names to 3 values. a, b, c = 3, 4, 5
        
      • I was able to get Gemini to do this with the following prompt: Write code to define positive integers a, b, and c of your own choosing in a single line
      • This line is harder to read and weirder to edit, but
      • There are many fewer lines.

Be sure to introduce yourselves!

Question #1

How do you decide how to express yourself in a constructed language?

• Think about a possible answer on your own
• Discuss your answers with the rest of the group
• Record a summary of each group’s discussion

If your initial answer is e.g. "I just do the first thing I think of" or "I just follow a guide" - dig deeper.

Why is that the first thing you think of?

How do you choose a guide?

How do you decide what prompt to give an AI?

Review:

• Homework 1 Pythagorean Triples
  • Calculate a², b², and c²
  • As with picking values, a few options:
    • Multi-cell
    • Multi-line / single-cell
    • Single-line
  • But an addition wrinkle: a² is not meaningful Python
    • This is an example of something that exists in a natural language but not a constructed langage.
    • Python, and many other programming languages, often lack to notion of "superscripts" or raised text.
    • Natural languages, which may have initially been written by hand on paper, can easily accomodate these features.

Review:

• Homework 1 Pythagorean Triples
  • a² is not meaningful Python
  • So what do we do?
  • "Squaring" can be thought of, in my mind, in two ways.
    • Multiply: I square some value by multipling that value by itself. a_squared = a * a
    • Exponentiation: I square some value by raising it to the second power. a_squared = a ** 2
    • I should also verify: a ** 2 == a * a

Review:

• Homework 1 Pythagorean Triples
  • a² is not meaningful Python
  • So what do we do?
  • "Squaring" can be thought of, in my mind, in two ways.
  • I gravitate toward multiplication.
    • In my mind: multiplication is easier that exponentiation, so I'll use that.
  • So I could write, perhaps: a_2, b_2, c_2 = a*a, b*b, c*c
  • Gemini did something quite different (for me): # prompt: Calculate a2, b2, and c2 a2 = a**2 b2 = b**2 c2 = c**2

Question #2

What are some reasons humans and machines may choose different ways to solve the same problems?

• Think about a possible answer on your own
• Discuss your answers with the rest of the group
• Record a summary of each group’s discussion

Did you use the same or different solutions than a machine might?

Review:

• Homework 1 Pythagorean Triples
  • Check to see if your three values form a Pythagorean Triple such that a² + b² = c².
  • Have Python print True or False to verify that you do, or do not, have a Pythagorean Triple defined.
  • Hint: You will need to use double and single equals as well as print()
    • We use double equals to determine the true/false value of the equality. a_2 + b_2 = c_2
    • We can use single equals again to assign the result to a variable. is_triple = a_2 + b_2 = c_2
    • We can use print() to "print" to true/false print(is_triple)
    • We could, of course, do everything in a single line print(a*a + b*b = c*c)
  • I asked for print make an important point: is_triple == print(is_triple) # this is "False"
    • Printing true/false and determining true/false are different things - it's good to keep this in mind.

Question #3

Reflect on what you learned about

• Python
• Thinking
• Language, and
• Machines

• Discuss your answers with the rest of the group
• Record a summary of each group’s discussion

Fake Functions

• Suppose we wish to check more than one triple.
  • We could, for example, have two Code cells:
  • In the first, we assign variables: a, b, c = 3, 4, 5
  • In the second, we print: print(a*a + b*b == c*c)
  • Then it is simply a matter of changing the variables and "running" two cells.
  
• Essentially, we have created a way to take three numbers and return a true/false value.
• We term this idea a function.

Functions

• Python contains the "lambda" keyword to make functions:
• Let's see it in action.

  Functionless	Function-ily

• It looks like this: triple_check = lambda a, b, c: print(a*a + b*b == c*c)
• Now: explore how functions work and can be used.

Recall:

• Exercise A.5 One or two equal signs.
• Select any two integers and assign them to any two variable names, such as "x" or "y"
  • It will help latter if the first value is much larger than the second, but you can always change latter.
• Calculate the integer "quotient" (the result of integer divison) and remainder of the two values
  • What operations should you use?
  • Store the result of each in a variable, for latter
• Use "double equals" to check if
  • the smaller value (say, y)
  • times the quotient (say, q)
  • plus the remainder (say, r)
  • is equal to the larger value (say, x)

For Today:

• Exercise A.6 A novel function.
  • Write a function that, given two numbers, say "a", "b", prints "True" if:
    • the second value (say, y)
    • times the quotient of the two values
    • plus the modulo of the two values
    • is equal to the first of the two values (say, x)
  • And prints "False" otherwise.

Question #4

What are some ways you think or act that feel like functions?

• Think about a possible answer on your own
• Discuss your answers with the rest of the group
• Record a summary of each group’s discussion

In your group, you may also wish to discuss how you feel about functions, Python, Opening Days, etc. Feel free to do so!

No Homework

• Be ready to begin the first week of your other classes!