5 ms·

if you genuinely understand something — really, truly understand it — then it doesn’t seem complicated and you can explain it rather simply Uh, no? Some things

by donaq 16y ago

if you genuinely understand something — really, truly understand it — then it doesn’t seem complicated and you can explain it rather simply Uh, no? Some things are inherently complex. Try explaining how the Y combinator works (not what it does - why it works) to a layman in simple terms. I don't think it can be done.

loup-vaillant 16y ago
OK, let's try. I think it can be done in 40 minutes, one hour tops. 15 minutes to explain what a function is: f1 : ℝ -> ℝ f1 = x |-> a × x + b f2 : (ℝ × ℝ) -> ℝ f2 = (x, y) |-> x + y - 1 f3 : ℝ -> ℝ -> ℝ f3 = (x, y) |-> x + y - 1 (I fear curryfication can't be skipped) f4 : (ℝ -> ℝ) -> ℝ -> ℝ f4 = f |-> x |-> f(x) f5 : ∀ a, ∀ b, (a -> b) -> a -> b f5 = f |-> x |-> f(x) (Polymorphic types may be left out, but I think they're important) Then 5 minutes to explain what a recursive function is: fac : ℕ -> ℕ fac = 0 |-> 1 x |-> x × fac(x - 1) Then 5 minutes to present a fix point combinator… fix : ∀ a, (a -> a) -> a fix = f |-> f (fix f) (or we could just say that a is ℕ) …and implement the factorial with it. ffac : (ℕ -> ℕ) -> ℕ -> ℕ ffac = f |-> 0 |-> 1 f |-> x |-> x × (f(x - 1)) fac : ℕ -> ℕ fac = fix(fac) We can do a step by step, normal order evaluation. If any question is asked, just say that evaluating the arguments first just won't work here. Then, maybe 5 more minutes to explain the concept of self reference without actually naming oneself: ~PM(~P) Where you assume that for any "printable" string X, PX is true, ~PX is false; that for any X such that XM(X) is printable, PM(X) is true; and that any printable string is true, or just don't have the form PX or ~PX. You will note that ~PM(~P) is true and not printable, because it basically says "I am not printable". This is an anonymous self reference. Finally, we can go on and present the Y combinator itself. It does the same thing as the "fix" combinator, we just have to show that's because there is an anonymous self reference somewhere. I think it can be done in 10 minutes. Phew. Done. And I didn't use any knowledge that a high school kid shouldn't have. Did I miss something?
- bhousel 16y ago
  > Did I miss something? Just the part about explaining it to a layman in simple terms..
  - loup-vaillant 16y ago
    Of course, the raw text above won't suffice. However, you will note that the notation I used is learned in high school. To me high school mathematics are quite accessible, though I understand that most people forget it as soon as they can. So, I just assume I will have to start from kindergarten arithmetic. And I had, in fact. I once explained functions to a 14 year old girl. I went as far as high order functions (function composition, I think), and she understood. I checked, she could answer my questions correctly. She was bright, but still. I think I was able to explain functions in rather simple terms. Now, if I can explain functions to a 14 year old girl, the rest is certainly doable.
    - jamesbritt 16y ago
      "Of course, the raw text above won't suffice." http://annieinfinite.com/wp-content/uploads/2009/10/then-a-miracle-occurs-cartoon.png http://annieinfinite.com/wp-content/uploads/2009/10/then-a-m...
- timwiseman 16y ago
  Phew. Done. And I didn't use any knowledge that a high school kid shouldn't have. Did I miss something? One thing. How long it takes most people to understand a concept. It took me much more than 15 minutes to understand what a function is in high school, and I have spent far more than 15 minutes explaining it to other people. And it definitely took more than 5 minutes to understand the concept of a recursive function. And you are assuming they have knowledge of concepts like string and whether or not they are printable...
  - loup-vaillant 16y ago
    Now, understanding a concept and grasping it to the point it becomes part of yourself are not the same thing. I don't expect people to remember the whole thing in less than an hour. Just to understand it, and being able to read supporting material without drowning. A string is a sequence of characters, and "printable" is some arbitrary property. I would of course say as much in my real explanation. Understand that my comment was just a sketch. I wonder If I shouldn't actually try to flesh it out. A video, maybe…
    - deleted 16y ago
      [deleted]
    - calcnerd256 16y ago
      Please do. I want something to point people to.
- tkahn6 16y ago
  "And I didn't use any knowledge that a high school kid shouldn't have" ...a high-school kid that has studied haskell maybe. Either you're being arrogant or you are very lucky to have gone to a school which teaches rudimentary type theory.
abecedarius 16y ago
I once explained it to a literature PhD, weak at math, who'd taught a course on writing under censorship. I told a short self-referential story whose structure mirrored the Y combinator's -- about tricking censors charged with banning self-referential stories. (Yes, many things are just complicated. But confusing explanations usually could be improved, just as confusing code usually could be lots clearer.)

by donaq 16y ago

loup-vaillant 16y ago

OK, let's try. I think it can be done in 40 minutes, one hour tops. 15 minutes to explain what a function is: f1 : ℝ -> ℝ f1 = x |-> a × x + b f2 : (ℝ × ℝ) -> ℝ f2 = (x, y) |-> x + y - 1 f3 : ℝ -> ℝ -> ℝ f3 = (x, y) |-> x + y - 1 (I fear curryfication can't be skipped) f4 : (ℝ -> ℝ) -> ℝ -> ℝ f4 = f |-> x |-> f(x) f5 : ∀ a, ∀ b, (a -> b) -> a -> b f5 = f |-> x |-> f(x) (Polymorphic types may be left out, but I think they're important) Then 5 minutes to explain what a recursive function is: fac : ℕ -> ℕ fac = 0 |-> 1 x |-> x × fac(x - 1) Then 5 minutes to present a fix point combinator… fix : ∀ a, (a -> a) -> a fix = f |-> f (fix f) (or we could just say that a is ℕ) …and implement the factorial with it. ffac : (ℕ -> ℕ) -> ℕ -> ℕ ffac = f |-> 0 |-> 1 f |-> x |-> x × (f(x - 1)) fac : ℕ -> ℕ fac = fix(fac) We can do a step by step, normal order evaluation. If any question is asked, just say that evaluating the arguments first just won't work here. Then, maybe 5 more minutes to explain the concept of self reference without actually naming oneself: ~PM(~P) Where you assume that for any "printable" string X, PX is true, ~PX is false; that for any X such that XM(X) is printable, PM(X) is true; and that any printable string is true, or just don't have the form PX or ~PX. You will note that ~PM(~P) is true and not printable, because it basically says "I am not printable". This is an anonymous self reference. Finally, we can go on and present the Y combinator itself. It does the same thing as the "fix" combinator, we just have to show that's because there is an anonymous self reference somewhere. I think it can be done in 10 minutes. Phew. Done. And I didn't use any knowledge that a high school kid shouldn't have. Did I miss something?

bhousel 16y ago
> Did I miss something? Just the part about explaining it to a layman in simple terms..
- loup-vaillant 16y ago
  Of course, the raw text above won't suffice. However, you will note that the notation I used is learned in high school. To me high school mathematics are quite accessible, though I understand that most people forget it as soon as they can. So, I just assume I will have to start from kindergarten arithmetic. And I had, in fact. I once explained functions to a 14 year old girl. I went as far as high order functions (function composition, I think), and she understood. I checked, she could answer my questions correctly. She was bright, but still. I think I was able to explain functions in rather simple terms. Now, if I can explain functions to a 14 year old girl, the rest is certainly doable.
  - jamesbritt 16y ago
    "Of course, the raw text above won't suffice." http://annieinfinite.com/wp-content/uploads/2009/10/then-a-miracle-occurs-cartoon.png http://annieinfinite.com/wp-content/uploads/2009/10/then-a-m...
timwiseman 16y ago
Phew. Done. And I didn't use any knowledge that a high school kid shouldn't have. Did I miss something? One thing. How long it takes most people to understand a concept. It took me much more than 15 minutes to understand what a function is in high school, and I have spent far more than 15 minutes explaining it to other people. And it definitely took more than 5 minutes to understand the concept of a recursive function. And you are assuming they have knowledge of concepts like string and whether or not they are printable...
- loup-vaillant 16y ago
  Now, understanding a concept and grasping it to the point it becomes part of yourself are not the same thing. I don't expect people to remember the whole thing in less than an hour. Just to understand it, and being able to read supporting material without drowning. A string is a sequence of characters, and "printable" is some arbitrary property. I would of course say as much in my real explanation. Understand that my comment was just a sketch. I wonder If I shouldn't actually try to flesh it out. A video, maybe…
  - deleted 16y ago
    [deleted]
  - calcnerd256 16y ago
    Please do. I want something to point people to.
tkahn6 16y ago
"And I didn't use any knowledge that a high school kid shouldn't have" ...a high-school kid that has studied haskell maybe. Either you're being arrogant or you are very lucky to have gone to a school which teaches rudimentary type theory.

abecedarius 16y ago

I once explained it to a literature PhD, weak at math, who'd taught a course on writing under censorship. I told a short self-referential story whose structure mirrored the Y combinator's -- about tricking censors charged with banning self-referential stories. (Yes, many things are just complicated. But confusing explanations usually could be improved, just as confusing code usually could be lots clearer.)