<p>I overheard in discussion tonight:</p>

<blockquote>
  <p>You know - you can represent a computer program as points on a Hilbert Curve. </p>
</blockquote>

<p>Is there a reference that explains this concept? I can't seem to Google for it. </p>

CC BY-SA 3.0
2014-08-28T13:35:51.993Z
I'm not sure about the Hilbert Curve reference, but since the Hilbert Curve is continuous and space-filling it's equivalent to representing a program as a point in the unit square. You can just as easily represent a computer program as a real number between (0,1) by transforming the program into binary, concatenating the digits, and prepending a $0.$
Foo Barrigno
CC BY-SA 3.0
2014-08-28T19:30:20.483Z
That would be a rational number, to be more precise. Of course, why not just use a natural number? (I'd say the question is too vague.)
Radu GRIGore
<constructive-mathematics><knowledge-representation>
Can I represent a computer program on a Hilbert Curve?
hawkeye
# Can I represent a computer program on a Hilbert Curve?

(Asked by: username_0 on 2014-08-28)

I overheard in discussion tonight:

> You know - you can represent a computer program as points on a Hilbert Curve.

Is there a reference that explains this concept? I can't seem to Google for it.

**Tags:** constructive-mathematics, knowledge-representation

> **Comments:**
> **username_1**: I'm not sure about the Hilbert Curve reference, but since the Hilbert Curve is continuous and space-filling it's equivalent to representing a program as a point in the unit square. You can just as easily represent a computer program as a real number between (0,1) by transforming the program into binary, concatenating the digits, and prepending a $0.$  
> **username_2**: That would be a rational number, to be more precise. Of course, why not just use a natural number? (I'd say the question is too vague.)  

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