I wonder if any of the more scientifically minded people on here could help me, please.

[mrzz]

I'm your average adult & I did daily & weekly sales records & weekly figures sheets the old way & only needed a calculator for the A.S.P.'s (average sales prices).

I am not judging people individually by the fact if they can instantly use those kinds of rulers or not. Most would be able to learn it, to begin with, and it is only natural that people shift to the most convenient/faster methods. Then it becomes a generational thing.

The question I asked my self is a collective one. Before I put it, a bit of a preamble:

Tools such as the ruler itself and the calculator are, in a way, crutches. They help you to perform a task, but at the same time people atrophy themselves by becoming dependent of it. If you look at those things in a collective, broader sense, it is a trade off that has been historically positive. After people started using calculators, surely on average people became less efficient in doing the basic calculations by themselves, and even understanding them. But the computational power got much larger, calculations could be done faster and people could focus their learning skills on other tasks which would be complex and include large calculations done by calculator (like an accountant dealing with giant and detailed paper spreadsheets). In other words, some "mental" muscles atrophy, while others develop. And the tools get more powerful, so the trade off is definitely positive.

Now I can go back to my question: will this trade off be always positive? Can we, at some point, start losing some very basic abilities that should be important in themselves? And, on the other hand, could our new tools start being less useful as tools and become just crutches? Reading Chris' post, realizing that in my case (and I am a person with a heavy scientific training) I had to stop and think just to follow his reasoning, I thought that just we got too damn lazy. Why do I need to know how to calculate if there are calculators? Why do I need to know the answer to a given question if "google knows"?

Why do I even need to know how to breathe if there are machines that can do it for me? At some point those questions become utterly idiotic, and the moment people are asking them seriously we are dead as a species.

 

[Horsa]

I am not judging people individually by the fact if they can instantly use those kinds of rulers or not. Most would be able to learn it, to begin with, and it is only natural that people shift to the most convenient/faster methods. Then it becomes a generational thing.

The question I asked my self is a collective one. Before I put it, a bit of a preamble:

Tools such as a ruler itself and the calculator are, in a way, crutches. They help you to perform a task, but at the same time people atrophy themselves by becoming dependent of it. If you look at those things in a collective, broader sense, it is a trade off that has been historically positive. After people started using calculators, surely on average people became less efficient in doing the basic calculations by themselves, and even understanding them. But the computational power got much larger, calculations could be done faster and people could focus their learning skills on other tasks which would be complex and include large calculations done by calculator (like an accountant dealing with giant and detailed paper spreadsheets). In other words, some "mental" muscles atrophy, while others develop. And the tools get more powerful, so the trade off is definitely positive.

Now I can go back to my question: will this trade off be always positive? Can we, at some point, start losing some very basic abilities that should be important in themselves? And, on the other hand, could our new tools start being less useful as tools and become just crutches? Reading Chris' post, realizing that in my case (and I am a person with a heavy scientific training) I had to stop and think just to follow his reasoning, I thought that just we got too damn lazy. Why do I need to know how to calculate if there are calculators? Why do I need to know the answer to a given question if "google knows"?

Why do I even need to know how to breathe if there are machines that can do it for me? At some point those questions become utterly idiotic, and the moment people are asking them seriously we are dead as a species.

O.K. I'm very sorry. I just felt the need to challenge your over-generalisation though I also personalised things.

I agree. I'm 1 of those people who will use all methods of doing things in order to stop myself from being lazy & I get a feeling of satisfaction from attempting to do all my calculations on paper 1st & succeeding with quite a lot before resorting to calculators & spreadsheets because I know that I'm capable of working them out myself. Sometimes though when you're under time pressure in an environment where productivity matters no matter how fast I manage to do things tools like calculators & spreadsheets can do these calculations faster. I like doing things the old way sometimes because doing things the old way keeps me going & stops me from feeling like a zombie.

Attempting to answer your question, I don't think so because although technology is highly sophisticated & increases productivity greatly it makes people lazy & feel like zombies & when these technologies fail for whatever reason everything comes to a standstill. I'll give a few personal examples, the 1st 2 tills I ever used were old ones, 1 where the till was only used to keep money & you got 1 price list a day & you had to work out all bills in your head (because no other paper except cashing up forms were available) & mark off using the 5 bar gate system on the price list what you sold so when it came to cashing up, another where you had to type everything in the till but if the till went down we worked things out in our heads & wrote receipts out in a receipt book, when I got taught how to use an epos system till I felt like a complete zombie so much so that sometimes I would type in the till that the customer gave me the correct money just to give me something to do because I knew I just switched off & made careless mistakes if I didn't do that every now & then & when the till went down I felt guilty that I couldn't keep serving customers as we didn't price stock individually like I used to do & everything was priced through the barcode-computer system & there was a perpetual inventory system in place which meant that if everything isn't scanned you can have lower levels of stock than is on the computer as all stock rotated off & sold is programmed into the computer which automatically orders stock which is too low though sometimes shop count & availability checks need to be done to check this perpetual inventory is correct so that stock levels are correct. Sometimes we need to know the answers to questions because it is more interesting to find the information for ourselves or be told that information than just to type said questions into ask or google topics & it stops us from feeling like zombies. I object to letting technology take over the way I do things & make me feel like a zombie. It's more interesting to pore over books & you find out lots of interesting things. I like to come out with what I know & remember because I don't want to be seen for something I'm not. I admit when I've found things out from reading books & use google as a last resort unlike some people. I realise Chris may have gone off on 1 with me because he thinks that I think of him as a google-brain which I don't & I'm very sorry to him if that's what he thought. I know there are lots of google-brains about though. I had to think twice too & I respect the fact that you're both scientists & I'm an average person. I also respect you both as people. I'm fascinated by what you both have to say sometimes. If I over-react at times it's because I think that at that time 1 of you has said something patronising or at least 1 of you has said something I found patronising though I know that is sometimes not the case & sometimes I've deserved it by acting daft. We have fun & fascinating conversations though & get on well most of the time. I've learnt a lot from you guys & am proud to be your friend. I'm also flattered that 2 gentlemen as capable as yourselves would want to talk to me.

I agree with what you say about these questions. I wouldn't quite agree that when we ask those questions seriously we are completely dead as a species but intellectually dead, yes. Aren't most people already intellectually dead by allowing these tools to "think" for us anyway?

 

[Horsa]

I think I've got the answer to a question I asked:

Why are hippikes, hippo & hippus all used to mean horse in Greek?

From seeing how they're used, hippikes is used as a word on its own in a phrase or sentence to mean horsemanship or horse, hippo is used as a prefix & hippus is used as a suffix.

 

[Chris Koziarz]

I am not judging people individually by the fact if they can instantly use those kinds of rulers or not. Most would be able to learn it, to begin with, and it is only natural that people shift to the most convenient/faster methods. Then it becomes a generational thing.

The question I asked my self is a collective one. Before I put it, a bit of a preamble:

Tools such as the ruler itself and the calculator are, in a way, crutches. They help you to perform a task, but at the same time people atrophy themselves by becoming dependent of it. If you look at those things in a collective, broader sense, it is a trade off that has been historically positive. After people started using calculators, surely on average people became less efficient in doing the basic calculations by themselves, and even understanding them. But the computational power got much larger, calculations could be done faster and people could focus their learning skills on other tasks which would be complex and include large calculations done by calculator (like an accountant dealing with giant and detailed paper spreadsheets). In other words, some "mental" muscles atrophy, while others develop. And the tools get more powerful, so the trade off is definitely positive.

Now I can go back to my question: will this trade off be always positive? Can we, at some point, start losing some very basic abilities that should be important in themselves? And, on the other hand, could our new tools start being less useful as tools and become just crutches? Reading Chris' post, realizing that in my case (and I am a person with a heavy scientific training) I had to stop and think just to follow his reasoning, I thought that just we got too damn lazy. Why do I need to know how to calculate if there are calculators? Why do I need to know the answer to a given question if "google knows"?

Why do I even need to know how to breathe if there are machines that can do it for me? At some point those questions become utterly idiotic, and the moment people are asking them seriously we are dead as a species.

Last paragraph is where you go too far with your vision of "automation" of everyday tasks. One cannot "forget" how to perform basic life supporting functions. They are involuntary, encoded very low, in brain stem up to lower cortex, and not in upper upper cortex.

I'd say we are not "lazy" but rather we are more specialised. The machines are here to help. And only those who chose to study the basics how different machines work, do understand them. These are usually people responsible for production of the machines. Rest of the society does not need to do anything but how to use the machines, relying on the experts knowledge and trusting their products work to specification. Trivial example: have u ever wondered how washing machine works? Maybe if you are as inquisitive as me (so I do) but an average person does not need to. Just throw the clothes in and add detergent and turn it on and forget. Why? To have time to concentrate on other specialised tasks you decided to study and be expert at. Inevitable side effect of specialisation. People invented google search engine, and only those people understand the inner working of the engine. Others don't need to and they rather rely on the technology working for them. Why? Because they have no time to study the details of the technology, they prefer to spend their time pursuing their own domain of knowledge they want to be experts at. And google search engine helps them to achieve their goals faster.

Now, certain pieces of technology such as slide rule naturally become outdated. Because other technology, such as calculators, embraces it by becoming more accurate and faster and cheaper at the same time. IMO, there is nothing wrong with forgetting old technology. I don't do it (maybe because I'm sentimental) but others do & it's fine. They don't necessarily forget the math behind it. I don't forget the math even though I never used slide rule. As I said, when I was shown how to use it by my older bro, I just laughed and thrown it to trash knowing it be just useless toy. But I use the math principles first developed for slide rules in my everyday work. E.g. in signal processing (including 2d signals suchas digital images) we use FFT to encode signals in frequency (rather than pixel amplitude) domain. Many signal processing operations, including image processing, become trivial additive operations that can be performed fast. While in pixel amplitude domain, said operations are not-trivial calculations involving heavy use of exp() function. So here you have the analogy of slide rule (albeit a very distant one) from our digital world. Math "trick" such as FFT helped to speedup the calculations needed.

 

[mrzz]

Last paragraph is where you go too far with your vision of "automation" of everyday tasks. One cannot "forget" how to perform basic life supporting functions. They are involuntary, encoded very low, in brain stem up to lower cortex, and not in upper upper cortex.

I'd say we are not "lazy" but rather we are more specialised. The machines are here to help. And only those who chose to study the basics how different machines work, do understand them. These are usually people responsible for production of the machines. Rest of the society does not need to do anything but how to use the machines, relying on the experts knowledge and trusting their products work to specification. Trivial example: have u ever wondered how washing machine works? Maybe if you are as inquisitive as me (so I do) but an average person does not need to. Just throw the clothes in and add detergent and turn it on and forget. Why? To have time to concentrate on other specialised tasks you decided to study and be expert at. Inevitable side effect of specialisation. People invented google search engine, and only those people understand the inner working of the engine. Others don't need to and they rather rely on the technology working for them. Why? Because they have no time to study the details of the technology, they prefer to spend their time pursuing their own domain of knowledge they want to be experts at. And google search engine helps them to achieve their goals faster.

Now, certain pieces of technology such as slide rule naturally become outdated. Because other technology, such as calculators, embraces it by becoming more accurate and faster and cheaper at the same time. IMO, there is nothing wrong with forgetting old technology. I don't do it (maybe because I'm sentimental) but others do & it's fine. They don't necessarily forget the math behind it. I don't forget the math even though I never used slide rule. As I said, when I was shown how to use it by my older bro, I just laughed and thrown it to trash knowing it be just useless toy. But I use the math principles first developed for slide rules in my everyday work. E.g. in signal processing (including 2d signals suchas digital images) we use FFT to encode signals in frequency (rather than pixel amplitude) domain. Many signal processing operations, including image processing, become trivial additive operations that can be performed fast. While in pixel amplitude domain, said operations are not-trivial calculations involving heavy use of exp() function. So here you have the analogy of slide rule (albeit a very distant one) from our digital world. Math "trick" such as FFT helped to speedup the calculations needed.

I guess that you are not still used to my hyperbolic style... the breathing example was to illustrate the point when (and if) we have tools for basically everything.

But I do agree with 100% of your points above. As I said, I think we are still in the phase where what I called a "trade off" is positive, and your arguments show it quite clearly that it is true. In your words, we have some ill effects of specialization, but they are largely compensated by all the benefits of it.

But my question is if it will be always like that. Two possibilities exists for the situation to get worse:

1) With tools getting better and better, people start to get lazy. In the past, tools allowed for one man to multiply the outcome of his work -- but he would still work a lot. Now, in some fields the actual amount of work is becoming smaller. What is the end result? I could use engineers as an example: calculators made them way more efficient. Nowadays you have a giant amount of good software that virtually does almost everything, so you have a generation of engineers who are very good software users but is starting to lose touch with the own subject matter. They understand less and less the physics behind everything, and, amazingly, you have way more structures collapsing in the XXI century than in the XX (due to engineering error). Yes, I am guessing, but I am pretty confident on my guess, at least regarding Brazil, which in fact has a good tradition in engineering. The example may be debatable but I guess you got the general point.

2) We lose track of the lower layers of technology: Example would be computer science. We have an army of programmers able to deal with high level languages, but the deeper you go, the fewer professionals you have. Computer science courses are more and more focused on higher lever, system design, so on and so forth. But everything happens at binary level, and somebody must be able to understand what is happening down there. It is not impossible that at some point this population becomes so small that some architectural change would imply in major difficulties, something like a really serious millennium bug" (or year 2000 problem). The banking industry in Brazil had sort of a similar problem. The lower levels of their computer systems were done in the 70's, using cobol language. A lot of those systems still run, and most of the new, more modern implementation are done on top of it. At some point years ago the number of programmers that new that language became extremely small, as it was and old language doomed to disappear, but it never did, and with banks needing to comply to more strict regulations, those systems needed a change here and there, so those guys suddenly became extremely valuable. Naturally, this financial incentive made the population grow again, but it really became critical at one point.

Pretty nice catch with the FFT analogy. By the way one day we could talk a bit more about it. I actually know quite well ordinary FT, even if I am a bit rusty now. But this is subject for another conversation...

 

[Horsa]

Pretty nice catch with the FFT analogy. By the way one day we could talk a bit more about it. I actually know quite well ordinary FT, even if I am a bit rusty now. But this is subject for another conversation...

I disagree & I'm going to ask the question & invite you to explain. What does F.F.T. stand for please?

 

[Horsa]

Last paragraph is where you go too far with your vision of "automation" of everyday tasks. One cannot "forget" how to perform basic life supporting functions. They are involuntary, encoded very low, in brain stem up to lower cortex, and not in upper upper cortex.

I'd say we are not "lazy" but rather we are more specialised. The machines are here to help. And only those who chose to study the basics how different machines work, do understand them. These are usually people responsible for production of the machines. Rest of the society does not need to do anything but how to use the machines, relying on the experts knowledge and trusting their products work to specification. Trivial example: have u ever wondered how washing machine works? Maybe if you are as inquisitive as me (so I do) but an average person does not need to. Just throw the clothes in and add detergent and turn it on and forget. Why? To have time to concentrate on other specialised tasks you decided to study and be expert at. Inevitable side effect of specialisation. People invented google search engine, and only those people understand the inner working of the engine. Others don't need to and they rather rely on the technology working for them. Why? Because they have no time to study the details of the technology, they prefer to spend their time pursuing their own domain of knowledge they want to be experts at. And google search engine helps them to achieve their goals faster.

Now, certain pieces of technology such as slide rule naturally become outdated. Because other technology, such as calculators, embraces it by becoming more accurate and faster and cheaper at the same time. IMO, there is nothing wrong with forgetting old technology. I don't do it (maybe because I'm sentimental) but others do & it's fine. They don't necessarily forget the math behind it. I don't forget the math even though I never used slide rule. As I said, when I was shown how to use it by my older bro, I just laughed and thrown it to trash knowing it be just useless toy. But I use the math principles first developed for slide rules in my everyday work. E.g. in signal processing (including 2d signals suchas digital images) we use FFT to encode signals in frequency (rather than pixel amplitude) domain. Many signal processing operations, including image processing, become trivial additive operations that can be performed fast. While in pixel amplitude domain, said operations are not-trivial calculations involving heavy use of exp() function. So here you have the analogy of slide rule (albeit a very distant one) from our digital world. Math "trick" such as FFT helped to speedup the calculations needed.

You mentioned that you know how a washing machine works. I'm interested. How does a washing machine work, please?

I'm also going to say I disagree with your idea of throwing away obsolete items as I collect some antiques. Some antiques are worth a lot. I like antiques. I possess a gramophone, a Victorian typewriter & a Victorian sewing-machine in good working order among many other old things.

 

[mrzz]

I disagree & I'm going to ask the question & invite you to explain. What does F.F.T. stand for please?

oh, I knew you would ask that... FFT stands for "Fast Fourier Transform". And now we got really, really, really technical and deep inside the realm of mathematics. This is a topic in general covered by post-graduate studies in science fields, so it basically takes the knowledge of such a course as needed background for a good comprehension of the topic. But we all know that neither you nor I would be satisfied with such an answer, so here we go... (but I will try a different approach).

Mathematics works (roughly speaking) in "layers". You can start by the very basic notion of counting -- which is sort of equivalent to the "natural numbers", 0,1,2,3... . That's our first layer.

Then, on top of that notion, you can build the idea of operations, first sums, then subtraction (defined as the opposite of sum). Subtraction leads to the notion of negative numbers, so we go from natural to integer numbers. On integer numbers you have an operation called multiplication. Then you get division, which is the opposite of multiplication. Now, division leads to fractions, and thus we have more numbers, not only the integers but the rational numbers. So on and so forth, the operations and families of numbers grow and grow, so we roughly now have what we can call arithmetic (and fields of numbers). That is our second layer.

Now we can start asking which number would yield a given result in a given operation. "Which number summed to 5 results in 8?" We have equations then. Equations can be simple as the example above, but even in the realm of simple arithmetic they can get complicated. I could go a bit further here but you guessed right, this is our third layer.

You can sort of generalize equations to get functions. For example, we go back to our equation above, which is x + 5 = 8. The answer is x =3. Now, what is the answer for x + 5 = 9? The answer is 4. And for x + 5 = 10? 6. There is pattern there, the general form would be x + 5 = y. So you have one number (y) which is a function of another (x). 95% of the world as we know it is described by simple (linear) function such as this one. Of course you can have much more complicated functions, involving squares, cubes, exponentials, etc.... That's our fourth layer.

Now we can start studying the functions themselves, how they behave, what happens if one variable (x or y) goes to zero, or to infinity, etc and etc. And we can define operations on functions (this is where is starts to get really complicated). Those operations are known as derivatives and integrals, something you study on a field called "calculus", which exists thanks to two gentlemen, one named Newton and the other Leibniz. They hated each other, by the way. That's our fifth layer.

With those operations that we study on calculus (integrals and derivatives) we can define what is called "transforms", which would roughly be like changes in a coordinate system -- for example, let us say you have an equation where the "X" is the distance from your home to the center of your town. But in another "coordinate system" maybe you would have not the distance to the center of your town, but to the center of a different one. In other words, you change what the "X" means. This example is actually not a good one, it is just to show the concept. Naturally there are whole universe of transforms, on a lot of contexts, and, you guessed, this is our sixth layer.

FFT is maybe on a seventh layer, because is a special type of transform. But, mathematics is such a strange thing. It looks quite specialized (and it is), but the wonderful thing is that people from two very different fields need exactly the same concept. Actually, the "more fundamental" one is FT, Fourier Transform, which is basic knowledge for people in Chris' area (signal processing, signal analysis) and in mine (quantum physics). Both communities now the field pretty well, even if we use a very differently terminology.

Chris will surely give very interesting examples of use of Fourier Transforms (FT) and Fast Fourier Transforms (FFT) in signal analysis, and believe me, it is extremely present in our lives. In quantum mechanics, you probably already heard about the famous Uncertainty Principle... well, it is basically a consequence of the fact that Fourier Transforms are the way by which you "transform" your knowledge of a physical system written in terms of one kind of physical quantity in to another.

Each of those layers is subject for years of study. Probably in each of those paragraphs I made some gross over-simplifications, but I hope technical readers will forgive me. I am actually still very far from answering the question, but I guess it helped to clarify the context.

 

[Horsa]

oh, I knew you would ask that... FFT stands for "Fast Fourier Transform". And now we got really, really, really technical and deep inside the realm of mathematics. This is a topic in general covered by post-graduate studies in science fields, so it basically takes the knowledge of such a course as needed background for a good comprehension of the topic. But we all know that neither you nor I would be satisfied with such an answer, so here we go... (but I will try a different approach).

Mathematics works (roughly speaking) in "layers". You can start by the very basic notion of counting -- which is sort of equivalent to the "natural numbers", 0,1,2,3... . That's our first layer.

Than, on top of that notion, you can build the idea of operations, first sums, then subtraction (defined as the opposite of sum). Subtraction leads to the notion of negative numbers, so we go from natural to integer numbers. On integer numbers you have an operation called multiplication. Then you get division, which is the opposite of multiplication. Now, division leads to fractions, and thus we have more numbers, not only the integers but the rational numbers. So on and so forth, the operations and families of numbers grow and grow, so we roughly now have what we can call arithmetic (and fields of numbers). That is our second layer.

Now we can start asking which number would yield a given result in a given operation. "Which number summed to 5 results in 8?" We have equations then. Equations can be simple as the example above, but even in the realm of simple arithmetic they can get complicated. I could go a bit further here but you guessed right, this is our third layer.

You can sort of generalize equations to get functions. For example, we go back to our equation above, which is x + 5 = 8. The answer is x =3. Now, what is the answer for x + 5 = 9? The answer is 4. And for x + 5 = 10? 6. There is pattern there, the general form would be x + 5 = y. So you have one number (y) which is a function of another (x). 95% of the world as we know it is described by simple (linear) function such as this one. Of course you can have much more complicated functions, involving squares, cubes, exponentials, etc.... That's our fourth layer.

Now we can start studying the functions themselves, how they behave, what happens if one variable (x or y) goes to zero, or to infinity, etc and etc. And we can define operations on functions (this is where is starts to get really complicated). Those operations are known as derivatives and integrals, something you study on a field called "calculus", which exists thanks to two gentlemen, one named Newton and the other Leibniz. They hated each other, by the way. That's our fifth layer.

With those operations that we study on calculus (integrals and derivatives) we can define what is called "transforms", which would roughly be like changes in a coordinate system -- for example, let us say you have an equation where the "X" is the distance from your home to the center of your town. But in another "coordinate system" maybe you would have not the distance to the center of your town, but to the center of a different one. In other words, you change what the "X" means. This example is actually not a good one, it is just to show the concept. Naturally there are whole universe of transforms, on a lot of contexts, and, you guessed, this is our sixth layer.

FFT is maybe on a seventh layer, because is a special type of transform. But, mathematics is such a strange thing. It looks quite specialized (and it is), but the wonderful thing is that people from two very different fields need exactly the same concept. Actually, the "more fundamental" one is FT, Fourier Transform, which is basic knowledge for people in Chris' area (signal processing, signal analysis) and in mine (quantum physics). Both communities now the field pretty well, even if we use a very differently terminology.

Chris will surely give very interesting examples of use of Fourier Transforms (FT) and Fast Fourier Transforms (FFT) in signal analysis, and believe me, it is extremely present in our lives. In quantum mechanics, you probably already heard about the famous Uncertainty Principle... well, it is basically a consequence of the fact that Fourier Transforms are the way by which you "transform" your knowledge of a physical system written in terms of one kind of physical quantity in to another.

Each of those layers is subject for years of study. Probably in each of those paragraphs I made some gross over-simplifications, but I hope technical readers will forgive me. I am actually still very far from answering the question, but I guess it helped to clarify the context.

O.K. Thank you very much for the explanation & simplifying it for me instead of just telling me I wouldn't understand. I really appreciate it & understand your points. I also realise how hard it must have been for you to simplify complicated things so much & to explain how I wouldn't be able to understand without patronising me or making me feel as though I was being patronised or feel insulted. You succeeded.

 

[Horsa]

Icefish so-called because they live in the icy waters of the arctic have no red blood cells. Scientists are studying them to see if they could give them a clue about how to cure leukaemia. Do you think they'll ever find a cure?

 

[britbox]

I'd say we are not "lazy" but rather we are more specialised. The machines are here to help. And only those who chose to study the basics how different machines work, do understand them. These are usually people responsible for production of the machines. Rest of the society does not need to do anything but how to use the machines, relying on the experts knowledge and trusting their products work to specification. Trivial example: have u ever wondered how washing machine works? Maybe if you are as inquisitive as me (so I do) but an average person does not need to. Just throw the clothes in and add detergent and turn it on and forget. Why? To have time to concentrate on other specialised tasks you decided to study and be expert at. Inevitable side effect of specialisation. People invented google search engine, and only those people understand the inner working of the engine. Others don't need to and they rather rely on the technology working for them. Why? Because they have no time to study the details of the technology, they prefer to spend their time pursuing their own domain of knowledge they want to be experts at. And google search engine helps them to achieve their goals faster.

Now, certain pieces of technology such as slide rule naturally become outdated. Because other technology, such as calculators, embraces it by becoming more accurate and faster and cheaper at the same time. IMO, there is nothing wrong with forgetting old technology. I don't do it (maybe because I'm sentimental) but others do & it's fine. They don't necessarily forget the math behind it. I don't forget the math even though I never used slide rule. As I said, when I was shown how to use it by my older bro, I just laughed and thrown it to trash knowing it be just useless toy. But I use the math principles first developed for slide rules in my everyday work. E.g. in signal processing (including 2d signals suchas digital images) we use FFT to encode signals in frequency (rather than pixel amplitude) domain. Many signal processing operations, including image processing, become trivial additive operations that can be performed fast. While in pixel amplitude domain, said operations are not-trivial calculations involving heavy use of exp() function. So here you have the analogy of slide rule (albeit a very distant one) from our digital world. Math "trick" such as FFT helped to speedup the calculations needed.

We've passed the tipping point where automation is here to help... we're in the realm where automation is here to replace.

 

[Chris Koziarz]

oh, I knew you would ask that... FFT stands for "Fast Fourier Transform". And now we got really, really, really technical and deep inside the realm of mathematics. This is a topic in general covered by post-graduate studies in science fields, so it basically takes the knowledge of such a course as needed background for a good comprehension of the topic. But we all know that neither you nor I would be satisfied with such an answer, so here we go... (but I will try a different approach).

Mathematics works (roughly speaking) in "layers". You can start by the very basic notion of counting -- which is sort of equivalent to the "natural numbers", 0,1,2,3... . That's our first layer.

Then, on top of that notion, you can build the idea of operations, first sums, then subtraction (defined as the opposite of sum). Subtraction leads to the notion of negative numbers, so we go from natural to integer numbers. On integer numbers you have an operation called multiplication. Then you get division, which is the opposite of multiplication. Now, division leads to fractions, and thus we have more numbers, not only the integers but the rational numbers. So on and so forth, the operations and families of numbers grow and grow, so we roughly now have what we can call arithmetic (and fields of numbers). That is our second layer.

Now we can start asking which number would yield a given result in a given operation. "Which number summed to 5 results in 8?" We have equations then. Equations can be simple as the example above, but even in the realm of simple arithmetic they can get complicated. I could go a bit further here but you guessed right, this is our third layer.

You can sort of generalize equations to get functions. For example, we go back to our equation above, which is x + 5 = 8. The answer is x =3. Now, what is the answer for x + 5 = 9? The answer is 4. And for x + 5 = 10? 6. There is pattern there, the general form would be x + 5 = y. So you have one number (y) which is a function of another (x). 95% of the world as we know it is described by simple (linear) function such as this one. Of course you can have much more complicated functions, involving squares, cubes, exponentials, etc.... That's our fourth layer.

Now we can start studying the functions themselves, how they behave, what happens if one variable (x or y) goes to zero, or to infinity, etc and etc. And we can define operations on functions (this is where is starts to get really complicated). Those operations are known as derivatives and integrals, something you study on a field called "calculus", which exists thanks to two gentlemen, one named Newton and the other Leibniz. They hated each other, by the way. That's our fifth layer.

With those operations that we study on calculus (integrals and derivatives) we can define what is called "transforms", which would roughly be like changes in a coordinate system -- for example, let us say you have an equation where the "X" is the distance from your home to the center of your town. But in another "coordinate system" maybe you would have not the distance to the center of your town, but to the center of a different one. In other words, you change what the "X" means. This example is actually not a good one, it is just to show the concept. Naturally there are whole universe of transforms, on a lot of contexts, and, you guessed, this is our sixth layer.

FFT is maybe on a seventh layer, because is a special type of transform. But, mathematics is such a strange thing. It looks quite specialized (and it is), but the wonderful thing is that people from two very different fields need exactly the same concept. Actually, the "more fundamental" one is FT, Fourier Transform, which is basic knowledge for people in Chris' area (signal processing, signal analysis) and in mine (quantum physics). Both communities now the field pretty well, even if we use a very differently terminology.

Chris will surely give very interesting examples of use of Fourier Transforms (FT) and Fast Fourier Transforms (FFT) in signal analysis, and believe me, it is extremely present in our lives. In quantum mechanics, you probably already heard about the famous Uncertainty Principle... well, it is basically a consequence of the fact that Fourier Transforms are the way by which you "transform" your knowledge of a physical system written in terms of one kind of physical quantity in to another.

Each of those layers is subject for years of study. Probably in each of those paragraphs I made some gross over-simplifications, but I hope technical readers will forgive me. I am actually still very far from answering the question, but I guess it helped to clarify the context.

Thanks mrzz for nicely explaining the basics, so I don't need to do it and can start from where you left.

The best way to understand the FT, the analog precursor of DFT (Discrete FT), is to draw a picture how Joseph Fourier understood it 200y ago.
FT is about decomposition of a signal (e.g. a time series of some value, where time runs on X axis and values are plotted on y axis) into a set of "perfect waves", i.e. the sine/cosine functions of a given amplitude, frequencies.
I found a decent picture here:
https://cdn.britannica.com/77/61777-004-EB9FB008.jpg
Therein you can see that a simple signal such as a step function (row 1) can be approximated by superposing several sine waves with different magnitude and frequencies. The picture shows only an approximation down to third harmonic, but you can imagine that by adding more and more tiny harmonics down to infinity you eventually arrive at perfect approximation of the input function (step function in this trivial case). Joseph proved that you can do such decomposition of every periodic input function. You can do it analytically for known periodic functions.
The only difference of FT and DFT is that the input signal of DFT is digital rather than analog, e.g. a time series of values, obtained by "sampling" the original analog signal at constant interval, e.g. every millisecond. So, instead of having a function, we have a series (many millions) of values and you can imagine the original function by connecting the neighbouring points in a series. No need to guess that everything is kept in such digital form today, e.g. audio signals, temperature history, images. The FFT is the ingenious algorithm that calculates DFT of any digital signal. FFT can run on single dimensional data, such as audio signal; or on multi-dimensional data; such as image (2D) or a scene in Euclidean space (3D).

I'm not going to explain the difference between FT and DFT calculation. I'll just mention that DFT calculation must be very efficient so that computers can perform it in reasonable time given large amount of input data (typically many million samples). That's why the ingenious FFT algorithm is called "fast". The output of FFT is series of frequencies, i.e. each point in the output data represents the magnitude of a sinus wave of a given frequency, where frequency is on the X axis and magnitude is on Y axis. E.g. for the simple step function in the picture above, the FFT output to the third approximation shown would include three points:
- 1Hz (X coordinate) and full amplitude, say 1 (Y coordinate), representing first harmonic
- 2Hz (X coordinate) and half full amplitude, say 1/2 (Y coordinate) representing second harmonic
- 4Hz (X coordinate) and full amplitude, say 1/4 (Y coordinate) representing third harmonic
More complex input would result in more complex picture (in frequency/amplitude) where points form some interesting images.

Why do we do such transform? Because complex signals are much easier to understand when viewed as a collection of frequencies. I'll give the most trivial example: analysis of music. As we know, music a collection of various tones played/sung in different pitches. The basic C7 major cord, consists of 4 tones: C1 E1 G1 C2 (in first octave) each tone defined by its unique frequency, played at the same time. When you look at the superposition of sound waves resulting from C7 cord, you have no idea what the signal represents. However, when you do FFT of that signal you get just 4 points on a frequency line: from 32.70Hz (representing C1) to 65.41Hz (representing C2) and same amplitude (if played correctly). After such transform, the computer has much easier time recognising the input signal as C7 cord in first octave.

I could go on with many examples, from temperature analysis (such as T proxies obtained from ice cores in Antarctica), image enhancement, to data analysis of mass spectrometer, but sorry no time to do it here. Enough to say, every scientist in 21st century cannot call himself as such if s/he does not use FFT to analyse their data. E.g. the mentioned T proxies obtained from ice cores in Antarctica:
https://www.e-education.psu.edu/ear...du.earth104/files/Unit1/Mod4/earth104_pic.jpg
have been FFTed to find out the major harmonic frequencies of the signals. The output in frequency domain:
https://www.e-education.psu.edu/ear...psu.edu.earth104/files/Unit1/Mod5/vostok2.jpg
confirmed the 3 major periods of ~100ky, 40ky and 25ky, of perturbations of Earth orbit (the three peaks of the signal).
(I think these pictures from PSU have been assembled by my friend Michael Mann)

As we know, said perturbations are responsible for climate changes resulting in onsets of ice ages. This example alone teaches us that whatever field you work on and whatever data you have, if u want to analyse your data first thing you do is FFT, and the output will tell you a lot more about the nature (mainly periodicity) of your signal.

 

[Chris Koziarz]

You mentioned that you know how a washing machine works. I'm interested. How does a washing machine work, please?

I'm also going to say I disagree with your idea of throwing away obsolete items as I collect some antiques. Some antiques are worth a lot. I like antiques. I possess a gramophone, a Victorian typewriter & a Victorian sewing-machine in good working order among many other old things.

This is quite simple to explain.

Washing machine is a box containing a bug drum, main drum motor, pump motor, various valves and relays. The heart of the machine is an electronic board with a bunch of timer modules, that are pre-programmed to switch on/off the relays, according to given washing cycle. There are only few (say dozen) washing cycles selected by user pressing buttons, but the electronic board is responsible to turn the relays on/off in specific sequence and time intervals accordingly. Various relays are controlling: opening/closing inlet water valves, turning the main motor to spin the drum at various speeds, turning on the heater element to bring water T to specified value, finally turning the pump to empty dirty water. That's the simplest overview.

There are also sensors that input the env data to the board, and in this case the board waits indefinitely until the signal reaches the specified value. The input env data is: water T, water level (or simply the weight of the full drum that approximates the amount of water in it), sometimes the detergent level, but usually user is responsible for measuring the amount detergent.

If anything can go wrong with a modern washer, it;s usually an electronic timer module. If the timer stops working (does not produce signal after a given time elapsed) the machine "hangs" and does not proceed to the next step. Also faulty relays/sensors can result in no water coming in, no water heating or overheating, etc. E.g.: when everything is stopped & water's boiling inside because the board does not proceed with turning off the heater & spinning the drum, it can be the board did not receive the signal from the T sensor. Newer boards have some diagnostics encoded in, so that they do not allow to be "stuck" in such stupid, energy sapping, dangerous state. Theee newer boards have a "timeout" for heating and other env-dependent operations to complete. If the operation does not complete at a given timeout, the board stops the washing process and displays something like "Exx" (an error code).

 

[Chris Koziarz]

We've passed the tipping point where automation is here to help... we're in the realm where automation is here to replace.

Nice optimist thinking as opposed to mrzz's scary vision. Yes I understand the problems of shifting expertise he points (especially in light of recent mining disasters in Brazil) but I do believe in a one way improvements the technological innovations bring to life. It is unlikely that humankind as a whole "forgets" the basis of their technology and is doomed as a result. The market mechanisms will always work to produce the financial incentives for the experts in any technology. The expert population will be maintained at required level throughout everywhere, coming from different countries if required (unless stupid politicians prevent that), there are 7 billion people worldwide.

 

[Horsa]

Thanks mrzz for nicely explaining the basics, so I don't need to do it and can start from where you left.

The best way to understand the FT, the analog precursor of DFT (Discrete FT), is to draw a picture how Joseph Fourier understood it 200y ago.
FT is about decomposition of a signal (e.g. a time series of some value, where time runs on X axis and values are plotted on y axis) into a set of "perfect waves", i.e. the sine/cosine functions of a given amplitude, frequencies.
I found a decent picture here:
https://cdn.britannica.com/77/61777-004-EB9FB008.jpg
Therein you can see that a simple signal such as a step function (row 1) can be approximated by superposing several sine waves with different magnitude and frequencies. The picture shows only an approximation down to third harmonic, but you can imagine that by adding more and more tiny harmonics down to infinity you eventually arrive at perfect approximation of the input function (step function in this trivial case). Joseph proved that you can do such decomposition of every periodic input function. You can do it analytically for known periodic functions.
The only difference of FT and DFT is that the input signal of DFT is digital rather than analog, e.g. a time series of values, obtained by "sampling" the original analog signal at constant interval, e.g. every millisecond. So, instead of having a function, we have a series (many millions) of values and you can imagine the original function by connecting the neighbouring points in a series. No need to guess that everything is kept in such digital form today, e.g. audio signals, temperature history, images. The FFT is the ingenious algorithm that calculates DFT of any digital signal. FFT can run on single dimensional data, such as audio signal; or on multi-dimensional data; such as image (2D) or a scene in Euclidean space (3D).

I'm not going to explain the difference between FT and DFT calculation. I'll just mention that DFT calculation must be very efficient so that computers can perform it in reasonable time given large amount of input data (typically many million samples). That's why the ingenious FFT algorithm is called "fast". The output of FFT is series of frequencies, i.e. each point in the output data represents the magnitude of a sinus wave of a given frequency, where frequency is on the X axis and magnitude is on Y axis. E.g. for the simple step function in the picture above, the FFT output to the third approximation shown would include three points:
- 1Hz (X coordinate) and full amplitude, say 1 (Y coordinate), representing first harmonic
- 2Hz (X coordinate) and half full amplitude, say 1/2 (Y coordinate) representing second harmonic
- 4Hz (X coordinate) and full amplitude, say 1/4 (Y coordinate) representing third harmonic
More complex input would result in more complex picture (in frequency/amplitude) where points form some interesting images.

Why do we do such transform? Because complex signals are much easier to understand when viewed as a collection of frequencies. I'll give the most trivial example: analysis of music. As we know, music a collection of various tones played/sung in different pitches. The basic C7 major cord, consists of 4 tones: C1 E1 G1 C2 (in first octave) each tone defined by its unique frequency, played at the same time. When you look at the superposition of sound waves resulting from C7 cord, you have no idea what the signal represents. However, when you do FFT of that signal you get just 4 points on a frequency line: from 32.70Hz (representing C1) to 65.41Hz (representing C2) and same amplitude (if played correctly). After such transform, the computer has much easier time recognising the input signal as C7 cord in first octave.

I could go on with many examples, from temperature analysis (such as T proxies obtained from ice cores in Antarctica), image enhancement, to data analysis of mass spectrometer, but sorry no time to do it here. Enough to say, every scientist in 21st century cannot call himself as such if s/he does not use FFT to analyse their data. E.g. the mentioned T proxies obtained from ice cores in Antarctica:
https://www.e-education.psu.edu/ear...du.earth104/files/Unit1/Mod4/earth104_pic.jpg
have been FFTed to find out the major harmonic frequencies of the signals. The output in frequency domain:
https://www.e-education.psu.edu/ear...psu.edu.earth104/files/Unit1/Mod5/vostok2.jpg
confirmed the 3 major periods of ~100ky, 40ky and 25ky, of perturbations of Earth orbit (the three peaks of the signal).
(I think these pictures from PSU have been assembled by my friend Michael Mann)

As we know, said perturbations are responsible for climate changes resulting in onsets of ice ages. This example alone teaches us that whatever field you work on and whatever data you have, if u want to analyse your data first thing you do is FFT, and the output will tell you a lot more about the nature (mainly periodicity) of your signal.

Thank you very much for your information. I think I get it now. Those diagrams look similar to the E.C.G. & E.E.G. signals & diagrams I see on medical programs.

 

[Horsa]

This is quite simple to explain.

Washing machine is a box containing a bug drum, main drum motor, pump motor, various valves and relays. The heart of the machine is an electronic board with a bunch of timer modules, that are pre-programmed to switch on/off the relays, according to given washing cycle. There are only few (say dozen) washing cycles selected by user pressing buttons, but the electronic board is responsible to turn the relays on/off in specific sequence and time intervals accordingly. Various relays are controlling: opening/closing inlet water valves, turning the main motor to spin the drum at various speeds, turning on the heater element to bring water T to specified value, finally turning the pump to empty dirty water. That's the simplest overview.

There are also sensors that input the env data to the board, and in this case the board waits indefinitely until the signal reaches the specified value. The input env data is: water T, water level (or simply the weight of the full drum that approximates the amount of water in it), sometimes the detergent level, but usually user is responsible for measuring the amount detergent.

If anything can go wrong with a modern washer, it;s usually an electronic timer module. If the timer stops working (does not produce signal after a given time elapsed) the machine "hangs" and does not proceed to the next step. Also faulty relays/sensors can result in no water coming in, no water heating or overheating, etc. E.g.: when everything is stopped & water's boiling inside because the board does not proceed with turning off the heater & spinning the drum, it can be the board did not receive the signal from the T sensor. Newer boards have some diagnostics encoded in, so that they do not allow to be "stuck" in such stupid, energy sapping, dangerous state. Theee newer boards have a "timeout" for heating and other env-dependent operations to complete. If the operation does not complete at a given timeout, the board stops the washing process and displays something like "Exx" (an error code).

Thank you very much for the information. It's fascinating. Like you said before though most people don't have to know how washing machines work just how to use them & who to call (if they have their appliances under warranty/extended warranty) if they break down or where to buy other washing machines. They make washing a lot quicker & easier as people can do other things at the same time, e.g. I once read 189 pages of Pride & Prejudice while washing. I've done washing the old way & all that scrubbing could be hard. My parents wanted to show me how hard it was in Grandma's time once so bought a block of carbolic soap from Haworth (which is supposed to be Bronte country but Charlotte was born in Thornton & Patrick & Maria came from Ireland as well as the fact that the umlaut which is supposed to be over the o in their surname suggests German origins, cut it into the right size pieces & got me scrubbing. It was hard work. That carbolic soap was good & lasted ages.

 

[Horsa]

I found out the answer to a question I asked you guys when chatting to someone. The question was "they're replacing our copper gas pipes with plastic ones as they say they're stronger. Plastic breaks easily so how can plastic gas pipes be stronger than copper ones?". It turns out that these plastic gas pipes are reinforced with metal.

 

[Horsa]

Very true but I could not help but to think about a book I recently discovered (and bought, still could not read it):

https://books.google.com.br/books/a...p_read_button&redir_esc=y#v=onepage&q&f=false

Amazing, isn't it?

I read about that book in a local newspaper this morning. It states that humans have 6 basic emotions & ways of showing them but they're not always easy to read in others as people can sometimes hide emotions & we have to decipher them. I might try to get a copy. Please tell me what you think of it when you've finished as it sounds interesting as you probably guessed from remembering me telling you that I enjoyed reading Daniel Goleman's emotional intelligence & destructive emotions & how to deal with them.

 

[Horsa]

What are gluons, please?

 

[mrzz]

Basically "particles" that are responsible for keeping some other, "larger" sub -atomic particles together. But at those scales things are not "black and white", the existence of such particles is different from the existence of the macroscopic bodies that we know in day to day life. At the end of the day you have a lot of complicated equations and you interpret some solutions to those equations as a particle (when some conditions are met).