Making Machines : Introduction
Machines are now ubiquitous but once they were just thoughts in a crazy man's mind. Well actually, many men but for our understanding there were three people who set the ball rolling.
1. Alan Turing
2. Alonzo Church
3. Kurt Godel
All these men were, in their own ways, trying to figure out a mathematical model for a machine. For all those readers who lost me here should think of a mathematical model as the way of describing anything around you with pen and paper. It's almost like taking notes but mathematics is the art of taking notes about your notes and doing all that till you make sense of what is possible by twisting what you know in ways you couldn't have directly imagined. Math is just a language and it's not necessary for all of us to think in that language.
My blog here is another effort among many to explain what "computation" means and how is it different and similar to the word "computer" we use every day now.
Think about what you would want a machine to do and try to break it down to the elements. When mathematicians were working on a machine model, all they were thinking is how to do complex calculations but you can choose to think differently. Maybe you want a computer to help you do your homework. It's important to remember that cars, cranes and other complex mechanical machines existed at the time(in some form or the other) when a computer was about to be invented. Therefore, I'm thinking if you were one of these men working on a better machine you wouldn't want it to lift weights or drive you home. So what is it that makes a computer different from all these machines ?
If you ask your computer to open a web browser, it will open it. If you ask it to do that 10 times, it will do it. If you ask it to shut down, it will shut down itself. Think of the many ways in which you command this complex machine to do your job. If you told your car via a steering wheel to take a left, it would do that but you would still be restricted by design decisions of the maker of the car. Is that also true for your computer ? Well, in part yes but you know that your computer is able to do more than your car.
The search for the answer to "how much more can machines do?" is how we stumbled upon this powerful device we call a computer. That's what these men were looking for; the answer to the question - "What are the things a machine can do?" and more importantly "What are the things it cannot do ?"
Now the hard part - how can you show the limit of the most powerful machine without making the most powerful machine ?
It seems unnatural to do something like that but maths can do that for you. Mathematics as a highly configurable language, has the power of describing a real system using some symbols and a set of rules on those symbols.
Although your computer does a lot of things, it does them by breaking complex questions down into simpler questions. If you ask it a question like what is "1+1" it would say "2" just because your machines knows what "1" and "2" is and it understands the meaning of the "+" you wrote between them. Hence, it has sufficient information to calculate the sum. It's useful to think about the questions a machine can't answer. The questions that cannot directly be answered from facts like what is "1" and what is "2" and what should I do when I see a "+" and two numbers around it. The first two facts are what we like to think of as data and the last one as operations (or functions) on that data.
This way of breaking things down into simpler things is fundamental to humans. We do it all the time. How do I get a get a gold in swimming - I need to get it, but to get it I need to practice. How much should I practice? Well that depends on how good I am currently and how good is the competition and how good they can get in the time they have. Now I decide I need to practice 15 hours in a week and then what do I do next? I plan my routine by breaking down my day into time slots for practice and arrange other things in my schedule....and all I had to do was win a gold, I'll give it all I have. Who cares if I plan the practice or not ? Right ?
The last thought is good if an individual makes his own decisions, this is what machines cannot do today for the simple reason that they do not have "moods" or "particular ways of thinking". They are just machines that follow a certain routine when they are told to and stop when they are ( or were in the past ) told to.
Imagine giving instructions to someone else who needs to win a gold medal. From the perspective of a coach, you decide the routine for what has to be done and you make sure that the person you are coaching follows it. This is what we are to machines, coaches. Although, a human may choose to follow or not follow your instructions partly or completely, but a machine always does follow them completely irrespective of what you said and whether its right or wrong. Therefore, its now on our shoulders, this responsibility of coaching a machine and doing it perfectly so that it succeeds in what to do.
Let's say you were able to make a machine win a gold in swimming and now you just want it to calculate the square root of 2 so that you can finish your homework. You'd say that's what your calculator can do but think of the number of different things you would want to do with machines and then think of how many machines you need ? More importantly, even you don't know what kind of help you will need from your friend machine in the future. Wouldn't it be good to know if you asked it to cross the road or save your life while you're doing that, which one of these can the machine do and which one it cannot ? I see you probably nodded just now and that's what these men also thought. That's why these men wanted to know the limit of things a machine can do to know how much can we push the bar and where we need to draw a line.
1. Alan Turing
2. Alonzo Church
3. Kurt Godel
All these men were, in their own ways, trying to figure out a mathematical model for a machine. For all those readers who lost me here should think of a mathematical model as the way of describing anything around you with pen and paper. It's almost like taking notes but mathematics is the art of taking notes about your notes and doing all that till you make sense of what is possible by twisting what you know in ways you couldn't have directly imagined. Math is just a language and it's not necessary for all of us to think in that language.
My blog here is another effort among many to explain what "computation" means and how is it different and similar to the word "computer" we use every day now.
Think about what you would want a machine to do and try to break it down to the elements. When mathematicians were working on a machine model, all they were thinking is how to do complex calculations but you can choose to think differently. Maybe you want a computer to help you do your homework. It's important to remember that cars, cranes and other complex mechanical machines existed at the time(in some form or the other) when a computer was about to be invented. Therefore, I'm thinking if you were one of these men working on a better machine you wouldn't want it to lift weights or drive you home. So what is it that makes a computer different from all these machines ?
If you ask your computer to open a web browser, it will open it. If you ask it to do that 10 times, it will do it. If you ask it to shut down, it will shut down itself. Think of the many ways in which you command this complex machine to do your job. If you told your car via a steering wheel to take a left, it would do that but you would still be restricted by design decisions of the maker of the car. Is that also true for your computer ? Well, in part yes but you know that your computer is able to do more than your car.
The search for the answer to "how much more can machines do?" is how we stumbled upon this powerful device we call a computer. That's what these men were looking for; the answer to the question - "What are the things a machine can do?" and more importantly "What are the things it cannot do ?"
Now the hard part - how can you show the limit of the most powerful machine without making the most powerful machine ?
It seems unnatural to do something like that but maths can do that for you. Mathematics as a highly configurable language, has the power of describing a real system using some symbols and a set of rules on those symbols.
Although your computer does a lot of things, it does them by breaking complex questions down into simpler questions. If you ask it a question like what is "1+1" it would say "2" just because your machines knows what "1" and "2" is and it understands the meaning of the "+" you wrote between them. Hence, it has sufficient information to calculate the sum. It's useful to think about the questions a machine can't answer. The questions that cannot directly be answered from facts like what is "1" and what is "2" and what should I do when I see a "+" and two numbers around it. The first two facts are what we like to think of as data and the last one as operations (or functions) on that data.
This way of breaking things down into simpler things is fundamental to humans. We do it all the time. How do I get a get a gold in swimming - I need to get it, but to get it I need to practice. How much should I practice? Well that depends on how good I am currently and how good is the competition and how good they can get in the time they have. Now I decide I need to practice 15 hours in a week and then what do I do next? I plan my routine by breaking down my day into time slots for practice and arrange other things in my schedule....and all I had to do was win a gold, I'll give it all I have. Who cares if I plan the practice or not ? Right ?
The last thought is good if an individual makes his own decisions, this is what machines cannot do today for the simple reason that they do not have "moods" or "particular ways of thinking". They are just machines that follow a certain routine when they are told to and stop when they are ( or were in the past ) told to.
Imagine giving instructions to someone else who needs to win a gold medal. From the perspective of a coach, you decide the routine for what has to be done and you make sure that the person you are coaching follows it. This is what we are to machines, coaches. Although, a human may choose to follow or not follow your instructions partly or completely, but a machine always does follow them completely irrespective of what you said and whether its right or wrong. Therefore, its now on our shoulders, this responsibility of coaching a machine and doing it perfectly so that it succeeds in what to do.
Let's say you were able to make a machine win a gold in swimming and now you just want it to calculate the square root of 2 so that you can finish your homework. You'd say that's what your calculator can do but think of the number of different things you would want to do with machines and then think of how many machines you need ? More importantly, even you don't know what kind of help you will need from your friend machine in the future. Wouldn't it be good to know if you asked it to cross the road or save your life while you're doing that, which one of these can the machine do and which one it cannot ? I see you probably nodded just now and that's what these men also thought. That's why these men wanted to know the limit of things a machine can do to know how much can we push the bar and where we need to draw a line.
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