6 ms·

>> If you see someone sorting papers and try to figure out why they are doing it inefficiently, that is mathematical inclination. Not really, I would say it wa

>> If you see someone sorting papers and try to figure out why they are doing it inefficiently, that is mathematical inclination. Not really, I would say it was a logical inclination not necessarily a mathematical one. And therein is the rub I see programming as logic and problem solving with little to no inherent math unless I am dealing with a mathematical problem. Kind of like the way writing books is not an inherently mathematical in nature even if quite a bit of math is involved in writing a mathematics text book.

lbrandy 18y ago
This is bordering on semantics. What's the difference between mathematical inclination and logical inclination? The field of computer programming has made a separation in alot of people's mind that simply didn't exist before. People, especially programmers, view mathematics far too narrowly because they lack historical context. George Boole was a mathematician. The logic textbooks are full of words that betray their background, e.g. the "lambda calculus". All of these things have their roots in mathematics. And before there was computer science degrees, these things -were- mathematics. I doubt, very seriously, that Djikstra would draw much of a distinction between "logical inclination" and "mathematical inclination". So while you might, the original context of the quote in question needs to be considered.
- bpyne 18y ago
  Agree fully with lbrandy's point. Just to add a little more, people seem to get confused between the expression of mathematical thoughts and having mathematical thoughts. Mathematical symbols are abbreviations for ideas that, if expressed in natural language, would become tedious. Mathematical thinking is something people do everyday. For example, parents have to use combinatorial optimization everyday to figure out a best strategy for running errands. Few parents are schooled to a formal expression of the mental processes they go through in determining a solution but they weigh different goals and optimize nonetheless. Oddly, a study that is all about exploration of ideas and abstraction has been narrowly defined in many people's minds. Hopefully mathematics educators can break these limited views in years to come.
- potatolicious 18y ago
  Maybe it's my engineering background, but I don't feel like this is semantics - it's unfair to categorize logical thinking as "mathematical" thinking. There are plenty of us from different backgrounds who are big on logic, and IMHO make great programmers. Mathematicians are far from the only ones who can think logically, and the term is at least somewhat misleading.
  - donaq 18y ago
    Uh, logic is a branch of mathematics. From wikipedia: Logic is the study of the principles of valid demonstration and inference. Logic is a branch of philosophy, a part of the classical trivium, as well as a branch of mathematics.
    - carbon8 18y ago
      potatolicious has a point. In fact, in universities, logic (formal logic, with symbols) is usually taught by philosophy departments.
      - donaq 18y ago
        That raises an interesting question, doesn't it? I wonder how many mathematicians turn out to be good programmers vs how many philosophers turn out to be good programmers?
        dkarl 18y ago
        From experience, I have concluded that whether mathematicians become good programmers depends on whether they have an engineering aesthetic. Mathematical elegance and engineering elegance are not exactly the same thing. A mathematically trivial solution can be a huge practical mess. Mathematicians with no engineering aesthetic can't see the difference and tend to produce big blobs of unmaintainable code. Mathematicians with an engineering aesthetic are some of the best programmers I've worked with. I've only worked with one philosopher. He's very creative and produces reams of working code, but new requirements always mean new reams of code. Everyone suspects there must be a lot of redundancy in his code, but then, nobody has needed to look, because it all works....
- carbon8 18y ago
  What's the difference between mathematical inclination and logical inclination? Logic is a strange area since it bridges fields, primarily math, philosophy, linguistics and computer science. In my experience, designing software more frequently taps into logic as applied to philosophical arguments and conceptual formal logic more than heavily mathematical areas of logic. The reason is that creating software is basically the process of taking something from the real world and reducing it to a series of logical components and relationships. This is pretty much the exact process for applying formal logic to philosophical questions. On the other hand, actually coding the software taps far more into the mathematical and linguistic aspects of formal logic, since it's involves piecing together units of mathematical logic to construct a logical machine. In practice, this whole process is obviously more nuanced, interconnected and filled with gray areas. It's also certainly possible to argue that all reasoning is math, but this isn't a new concept and dates back to Plato.

lbrandy 18y ago

This is bordering on semantics. What's the difference between mathematical inclination and logical inclination? The field of computer programming has made a separation in alot of people's mind that simply didn't exist before. People, especially programmers, view mathematics far too narrowly because they lack historical context. George Boole was a mathematician. The logic textbooks are full of words that betray their background, e.g. the "lambda calculus". All of these things have their roots in mathematics. And before there was computer science degrees, these things -were- mathematics. I doubt, very seriously, that Djikstra would draw much of a distinction between "logical inclination" and "mathematical inclination". So while you might, the original context of the quote in question needs to be considered.

bpyne 18y ago
Agree fully with lbrandy's point. Just to add a little more, people seem to get confused between the expression of mathematical thoughts and having mathematical thoughts. Mathematical symbols are abbreviations for ideas that, if expressed in natural language, would become tedious. Mathematical thinking is something people do everyday. For example, parents have to use combinatorial optimization everyday to figure out a best strategy for running errands. Few parents are schooled to a formal expression of the mental processes they go through in determining a solution but they weigh different goals and optimize nonetheless. Oddly, a study that is all about exploration of ideas and abstraction has been narrowly defined in many people's minds. Hopefully mathematics educators can break these limited views in years to come.
potatolicious 18y ago
Maybe it's my engineering background, but I don't feel like this is semantics - it's unfair to categorize logical thinking as "mathematical" thinking. There are plenty of us from different backgrounds who are big on logic, and IMHO make great programmers. Mathematicians are far from the only ones who can think logically, and the term is at least somewhat misleading.
- donaq 18y ago
  Uh, logic is a branch of mathematics. From wikipedia: Logic is the study of the principles of valid demonstration and inference. Logic is a branch of philosophy, a part of the classical trivium, as well as a branch of mathematics.
  - carbon8 18y ago
    potatolicious has a point. In fact, in universities, logic (formal logic, with symbols) is usually taught by philosophy departments.
    - donaq 18y ago
      That raises an interesting question, doesn't it? I wonder how many mathematicians turn out to be good programmers vs how many philosophers turn out to be good programmers?
      - dkarl 18y ago
        From experience, I have concluded that whether mathematicians become good programmers depends on whether they have an engineering aesthetic. Mathematical elegance and engineering elegance are not exactly the same thing. A mathematically trivial solution can be a huge practical mess. Mathematicians with no engineering aesthetic can't see the difference and tend to produce big blobs of unmaintainable code. Mathematicians with an engineering aesthetic are some of the best programmers I've worked with. I've only worked with one philosopher. He's very creative and produces reams of working code, but new requirements always mean new reams of code. Everyone suspects there must be a lot of redundancy in his code, but then, nobody has needed to look, because it all works....
carbon8 18y ago
What's the difference between mathematical inclination and logical inclination? Logic is a strange area since it bridges fields, primarily math, philosophy, linguistics and computer science. In my experience, designing software more frequently taps into logic as applied to philosophical arguments and conceptual formal logic more than heavily mathematical areas of logic. The reason is that creating software is basically the process of taking something from the real world and reducing it to a series of logical components and relationships. This is pretty much the exact process for applying formal logic to philosophical questions. On the other hand, actually coding the software taps far more into the mathematical and linguistic aspects of formal logic, since it's involves piecing together units of mathematical logic to construct a logical machine. In practice, this whole process is obviously more nuanced, interconnected and filled with gray areas. It's also certainly possible to argue that all reasoning is math, but this isn't a new concept and dates back to Plato.