proof that math can prove anything. which is why i stay away from it ... the circuit on the bench does not lie. no matter what the maths say.
proof that math can prove anything. which is why i stay away from it ... the circuit on the bench does not lie. no matter what the maths say.
As someone once said, the best maths is the maths you can use without reverting to deriving everything from first principles. But you need to understand the first principles so you don't violate them.
Example -1=1, without misuse of zeros, and in an example which can foul up frequency domain analysis of electronic circuits:
1: sqrt(-1) = sqrt(-1)
2: therefore sqrt(-1/1) = sqrt(1/-1)
3: therefore sqrt(-1)/sqrt(1) = sqrt(1)/sqrt(-1)
4: therefore sqrt(-1)*sqrt(-1) = sqrt(1)*sqrt(1)
5: therefore -1 = 1
QED
Almost everybody can correctly determine that the error is going from 2 to 3, but they can't say what the error is. I've only come across one person who could give the reason.
As someone once said, the best maths is the maths you can use without reverting to deriving everything from first principles. But you need to understand the first principles so you don't violate them.
Example -1=1, without misuse of zeros, and in an example which can foul up frequency domain analysis of electronic circuits:
1: sqrt(-1) = sqrt(-1)
2: therefore sqrt(-1/1) = sqrt(1/-1)
3: therefore sqrt(-1)/sqrt(1) = sqrt(1)/sqrt(-1)
4: therefore sqrt(-1)*sqrt(-1) = sqrt(1)*sqrt(1)
5: therefore -1 = 1
QED
Almost everybody can correctly determine that the error is going from 2 to 3, but they can't say what the error is. I've only come across one person who could give the reason.
Back before Christsmas I had PMs requesting that I show the error. Given the difficulty of formatting maths on this forum, it will be difficult, but I'll do my best.
Firstly, as any fule knos, "i" represents current, so I'll use the traditional "j" to be sqrt(-1), and I'll use "w" instead of omega=2*pi*f. Secondly, this kind of manipulation can arise when doing frequency domain analysis of circuits, where term such as 1/(R+jwL) are common. Thirdly, I'll note that MrFlibble's comment about using the Euler form is equivalent to using the complex conjugate described below.
The key is recognising that a full representation of a complex number is a+jb, and that sqrt(-1) is a special case when a=0 and b=1.
If we want to "get rid of the complex denominator" / "move the j to the top line" in 1/(a+jb) we have to multiply top and bottom by the complex conjugate (a-jb).
(1/(a+jb))*((a-jb)/(a-jb))
Multiplying out the numerator and denominator gives
(a-jb)/(a2-jab+jab+b2)
or
(a-jb)/(a2+b2)
Now for the special case where a=0 and b=1, we can see that 1/j = -j/1 , and that's why
sqrt(1/-1) != sqrt(1)/sqrt(-1)
And that's why despite "the best maths being the maths you can use without reverting to deriving everything from first principles", you need to understand the first principles so you don't violate them.
I hope that's all legible
As someone once said, the best maths is the maths you can use without reverting to deriving everything from first principles. But you need to understand the first principles so you don't violate them.
Example -1=1, without misuse of zeros, and in an example which can foul up frequency domain analysis of electronic circuits:
1: sqrt(-1) = sqrt(-1)
2: therefore sqrt(-1/1) = sqrt(1/-1)
3: therefore sqrt(-1)/sqrt(1) = sqrt(1)/sqrt(-1)
4: therefore sqrt(-1)*sqrt(-1) = sqrt(1)*sqrt(1)
5: therefore -1 = 1
QED
Almost everybody can correctly determine that the error is going from 2 to 3, but they can't say what the error is. I've only come across one person who could give the reason.
Back before Christsmas I had PMs requesting that I show the error. Given the difficulty of formatting maths on this forum, it will be difficult, but I'll do my best.
Firstly, as any fule knos, "i" represents current, so I'll use the traditional "j" to be sqrt(-1), and I'll use "w" instead of omega=2*pi*f. Secondly, this kind of manipulation can arise when doing frequency domain analysis of circuits, where term such as 1/(R+jwL) are common. Thirdly, I'll note that MrFlibble's comment about using the Euler form is equivalent to using the complex conjugate described below.
The key is recognising that a full representation of a complex number is a+jb, and that sqrt(-1) is a special case when a=0 and b=1.
If we want to "get rid of the complex denominator" / "move the j to the top line" in 1/(a+jb) we have to multiply top and bottom by the complex conjugate (a-jb).
(1/(a+jb))*((a-jb)/(a-jb))
Multiplying out the numerator and denominator gives
(a-jb)/(a2-jab+jab+b2)
or
(a-jb)/(a2+b2)
Now for the special case where a=0 and b=1, we can see that 1/j = -j/1 , and that's why
sqrt(1/-1) != sqrt(1)/sqrt(-1)
And that's why despite "the best maths being the maths you can use without reverting to deriving everything from first principles", you need to understand the first principles so you don't violate them.
I hope that's all legibleYou don't need to resort to anything so extensive. The simple fact is that the sqrt(1) is +/-1 so you could just put
sqrt(1) = sqrt(1)
therefore -1 = +1 as they are both the sqrt(1).
The misuse of math or other very factual system has long been misused to "prove" various scams
The misuse of math or other very factual system has long been misused to "prove" various scams
No.
While true, that neither explains the problem/solution nor illuminates the way in which it bites in s-plane (frequency domain) analysis. I refer you to my hint concerning 1/(R+jwL) for an example of the latter.
I'm not sure under what circumstances it is necessary to take complex roots in circuit analysis. Such a + b(jw) analysis is generally used in linear analysis of circuits and having a root function would be nonlinear.
In my own case. I was an EE student but switched to CompSci my SENIOR year. It was the mid 80's and I simply decided that I liked all the new exciting computer stuff more. I don't regret that decision, the 80s, 90s, and first decade of the 2000's were exciting times in IT and provided a very interesting career.
So, while I am not an EE, I ended up an IT professional for the last 20 years, but it was my original interest, and it and ham radio have made it my hobby. I don't remember everything from school, and lots of it is not all that up to day anyway probably, but it certainly provided a very good 'base' for my hobby electronics experimentation. In my hobby level electronics I am pretty sure I would fit your skills myself and I have never worked a single day as an EE or with electronics professionally, its all been an IT career for me.
For many people computer stuff is a hobby, for me at the skill level I have now, its almost too easy to do nearly anything IT related and it has become just a "job" that I don't want to do at home as well as work. So ham radio and electronics provide that same mental stimulation and challenge that computers used to provide me when I was young.
I do believe your best bet to find someone that would fit WOULD be either a hobbyist or maybe a retired EE who used to be technical but at some point got into mgmt, sales, consulting etc, but still has a love of electronics and would enjoy doing it again.
Frankly, I think you should have "Advanced Amateur Radio License" as a job requirement.
If you want a group of non-EE professionals who have serious electronics skills, hang around ham radio people.
Now for the special case where a=0 and b=1, we can see that 1/j = -j/1 , and that's why
sqrt(1/-1) != sqrt(1)/sqrt(-1)
I think North American education dramatically misses out somewhere on teaching math to kids when they are young or something. I found that number of people (engineers, programmers, accountants) that are scared of math among North Americans are drastically higher than let's say among Indians, Chinese or those who get Soviet education or those who went to school in Europe. I must say they usually catch up when they go to university but they go through so much pain and fear never goes away. It is like they had this drastic experience of drowning in backyard pool when they were kids and even though they can swim now fear is always with them.
Going back to reality vs mathematical abstraction - there is famous quote of Richard Freymann:
"physics is to mathematics as sex is to masturbation"
I think North American education dramatically misses out somewhere on teaching math to kids when they are young or something. I found that number of people (engineers, programmers, accountants) that are scared of math among North Americans are drastically higher than let's say among Indians, Chinese or those who get Soviet education or those who went to school in Europe. I must say they usually catch up when they go to university but they go through so much pain and fear never goes away. It is like they had this drastic experience of drowning in backyard pool when they were kids and even though they can swim now fear is always with them.
Going back to reality vs mathematical abstraction - there is famous quote of Richard Freymann:
"physics is to mathematics as sex is to masturbation"There has been a shift in priorities over the past 40 years away from numeracy and literacy (the 3 R's) and toward teamwork, "problem solving" and interpersonal skills as desired by employers.
In other words, they don't care if Jack can't add or subtract, read or write (since that can be done with hardware these days...) but must play well with others, do as he is told and follow the leader.
Interesting article here:
http://devlinsangle.blogspot.com/2015/01/your-fathers-mathematics-teaching-no.html
Simon, you should see the SA education system. At best they are proud that they are going back to making the pass level 50%, as opposed to the one for the last few years of 30% being a pass, or you just get bumped up if you are not even at that level. Not helped by an education department that cannot even provide little things like schoolbooks, teachers, schools............. But they do have a nice fancy new central office suite for the top levels, and all are driving department supplied luxury 4x4 vehicles.
A class diagram allows you to deconstruct the problem domain, see the connections, understand what is what. I've seen too much software that was written without the creator taking the time to understand all that.
IMNSHO experience, a class diagram is one of the least informative diagrams.
What is far more useful are:
- state diagrams, i.e. the Harel StateCharts. No, Mr NewGrad, FSMs aren't only usful for parsers
- interaction diagrams, i.e. the swimlanes. Especially useful in distributed systems, so that you can see overlapping processing
- and the name escapes me, but the diagram that shows which processing is done on which machine, and the communication mechanism
- proper use of parallelism design patterns, e.g. as embodied in Doug Lea's concurrency classes. No Mr NewGrad, you shouldn't be using wait(), notify(), synchronized, volatile
A class diagram allows you to deconstruct the problem domain, see the connections, understand what is what. I've seen too much software that was written without the creator taking the time to understand all that.
IMNSHO experience, a class diagram is one of the least informative diagrams.
What is far more useful are:
- state diagrams, i.e. the Harel StateCharts. No, Mr NewGrad, FSMs aren't only usful for parsers
- interaction diagrams, i.e. the swimlanes. Especially useful in distributed systems, so that you can see overlapping processing
- and the name escapes me, but the diagram that shows which processing is done on which machine, and the communication mechanism
- proper use of parallelism design patterns, e.g. as embodied in Doug Lea's concurrency classes. No Mr NewGrad, you shouldn't be using wait(), notify(), synchronized, volatile
bitch please, HW guys discussing SW design topic, is like white people calling eachother niggas
A class diagram allows you to deconstruct the problem domain, see the connections, understand what is what. I've seen too much software that was written without the creator taking the time to understand all that.
IMNSHO experience, a class diagram is one of the least informative diagrams.
What is far more useful are:
- state diagrams, i.e. the Harel StateCharts. No, Mr NewGrad, FSMs aren't only usful for parsers
- interaction diagrams, i.e. the swimlanes. Especially useful in distributed systems, so that you can see overlapping processing
- and the name escapes me, but the diagram that shows which processing is done on which machine, and the communication mechanism
- proper use of parallelism design patterns, e.g. as embodied in Doug Lea's concurrency classes. No Mr NewGrad, you shouldn't be using wait(), notify(), synchronized, volatile
bitch please, HW guys discussing SW design topic, is like white people calling eachother niggas
Do you have a coherent point to make, or are you just trolling?
BTW, it might be wise to be a little more humble, just in case your unstated presumptions turn out to be completely inaccurate.