I'm a technical writer and though nominally at retirement age, I intend to keep working for a few years as I find it interesting (especially since there's so much remote work available nowadays). I have just been recruited by an agency that provides articles for tech companies' blog sites and white papers on technical subjects, for example API's. Learning a lot through doing it. So I've decided to try and dip my toe in the water with programming. I think I'll start with javascript as I have at least some experience with HTML and CSS.

Why I tend to think people here are much younger than they are? I thought the same of universeness, who was a computer teacher. Nice that you intend to learn that still! I have read quite some stuff of you here. Sounds fresh and young, breaking with the "established" science. Anti-matterialistic (I'm a materialist myself, but I think all matter is litterally charged with unexplainable stuff). Keep it up!

Why thanks! Kind of you to say so.

So I've decided to try and dip my toe in the water with programming. — Wayfarer

Good luck, my friend. :smile:

I'm a materialist myself, but I think all matter is litterally charged with unexplainable stuff. — Cornwell1

Haha! That's it! We are miracle-charged! Made in heaven!

Yeah, I used to entertain my students with stories about the early days of computing.
Opcodes and operands, assembly codes, big valves switching on and off for 1 and 0.
punch cards (I had some metal ones to show them) and punch tape etc. Pages of daisy wheel printer paper, connected pages of thin paper, perforated on both sides, full of nothing but 1's and 0's with an error in one 16bit stream, on the 31st page of a printout of 100 pages. A 1 that should have been a 0.
They began to understand how error checking was quite hard in those days.

A friend at uni did his thesis on manipulating fractals. He produced some amazing looking flora type images based on ordering chaotic fractals using algorithms. Good stuff.

I thought the same of universeness, who was a computer teacher. — Cornwell1

:grin: :heart:

Ha Ha. Now, that's a brilliant piction(my word for picture with caption)! aint it the truth! best post I've seen since joining this forum.
Still laughing....... :lol: :lol: :lol:

Ha! "Science piction" movies. When subtitled.

What's the difference between = and :=? Say $f(x)=x^2$ and $f(x):=x^2$. And what's the difference with ≡, "identical to"?

Ha! "Science piction" movies. When subtitled. — Cornwell1

Yeah, but I just stole the word from the board game called 'Pictionary,' so I can't claim to be the originator.

What's the difference between = and :=? Say f(x)=x2f(x)=x2 and f(x):=x2f(x):=x2. And what's the difference with ≡, "identical to"? — Cornwell1

It depends, are you asking about what these mean in maths or computing or both?
The way they work is the same in both fields but their 'workings' are represented/emulated in Computing in a different way than they are in maths.
I don't know of a programming language that would have a code line, such as

f(x):=x^2

To me, with my computing hat on, this line is an incorrect use of the := operator.
With my maths hat on, it would also be incorrect to write this because use of := means that you are not writing an equation, you are writing an assignment expression. So it only makes sense if you are simply trying to say "I am assigning x^2 TO BE A FUNCTION OF X"

In computing, it would be more like:

REM subroutines
f(x);
LOCAL z;
LET z=x
LET z:=z*z
RETURN z

REM main program
INPUT x
y:= CALL f(x)
PRINT y
REM end program

In maths, as you know, the function f(x) = x^2 would graph as a parabolic curve.
A loop would be used within the above program to create the same thing on a computer screen.
So f(x) = x^2 to me in words says "a function/operation/process which can be equally represented by x^2 or the function of squaring a range of numbers, one after the other.
A function of x SUCH THAT we will square each value of x. Is to me, a balanced statement.
The := operator is only needed in computing because = is more commonly used as a true/false operator.

I have never come across the symbol ≡ in my maths or computing experience that I can recall.
but to me, identical means no difference at all. I don't see any difference between
x = x and x ≡ x

Perhaphs jgill, can offer better insight here, than I.

And what's the difference with ≡, "identical to"? — Cornwell1

$2x=3-4x$
Conditional equation, true only for select values of x

${{\left( x+1 \right)}^{2}}\equiv {{x}^{2}}+2x+1$
Identity, true for all or nearly all values of x

The latter isn't used much anymore.

Perhaphs jgill, can offer better insight here, than I. — universeness

Nope. You did a great job, buddy :cool:

Nope. You did a great job, buddy — jgill

:grin:

Hey seeing as you guys know computer science, answer me this question.

I posted a lnk to a documentary about Claude Shannon a few weeks back. Shannon is widely credited with coining the term 'bit' for 'binary digit' (although he always says one of his co-workers did it first.)

Anyway, never mind, my question is, did the earlier computers, such as ENIAC, not operate on binary digits? Shannon's paper was published in 1948 and ENIAC commenced operations in 1945. My knowledge of maths and computer science is rudimentary but I'm finding it hard to imagine how computers could operate on anything other than binary digits (leaving aside quantum computers, which I know I'll never fathom).

Anyway, never mind, my question is, did the earlier computers, such as ENIAC, not operate on binary digits? Shannon's paper was published in 1948 and ENIAC commenced operations in 1945. My knowledge of maths and computer science is rudimentary but I'm finding it hard to imagine how computers could operate on anything other than binary digits — Wayfarer

Earlier computers represented numbers in decimal. Here's an example. So, consider adding 4 to 128. 8 + 4 modulo 10 = 2. So only the bottom two vacuum tubes would be switched on in the third column. 8 + 4 > 10, so carry 1 to the second column. 2 + 1 modulo 10 = 3. So only the bottom three vacuum tubes would be switched on in the second column.

(leaving aside quantum computers, which I know I'll never fathom). — Wayfarer

Quantum computers use qubits which are able to represent bit values (0 and 1) in superposition.

I'm finding it hard to imagine how computers could operate on anything other than binary digits — Wayfarer

You are correct, they don't. All computers work on the basis of the binary system, including quantum computers, they just use Qbits which have three states instead of two (the third state is based on quantum entanglement, so the system is still basically binary).
You could use say trinary but parity checking and error checking would be a lot more complicated.
Consider an input cable carrying an electric signal.
A binary digit 1 is recorded if a voltage on the wire is >0 and < 5 volts.
This happens within a set time pulse.
If no voltage is detected on the line then a 0 is recorded.
This is a simplistic view as there are other elements such as start bits and stop bits etc
If you introduce a trinary system then you need to represent 0,1 and 2. A three state system.
So you would have to have a range of voltages which represent a 2, say 5v....<8V.
Things get much more complicated due to this.
any loss in voltage (due to weather, interference, degradation, surge etc) can turn a 1 into a zero or a 0 into a 1) Most of these errors can be caught by parity checking (which I won't go into for now)
But if you have a third state, then a 2 can fall to a 1 or a 0 etc, much more complicated.
So binary is best.

Oh, I forgot to type, I don't know who coined the phrase BInary digiT (bit). I've never heard of Claude Shannon, so there you go, you know stuff I don't about a subject I have an honors degree in and taught for 30 years.

I think the earliest stand alone computers worked on the same principle, for the same reason, that more than two states would have added too much complexity. I think this was even the case with the difference engine created by Babbage.

I've never heard of Claude Shannon, — universeness

Thanks both for the illuminating answers. That top reference hits the nail right on the head.

Claude Shannon is often mentioned on this forum. He wrote a paper on the transmission of electronic information and error correction which is considered one of the fundamental papers of the information age. His work made compression possible (among many other things). But it also has deep philosophical implications, according to a lot of people anyway. And last but not least he was a fascinating character, very humorous and known for building crazy inventions, like a mechanical calculator that operated on roman numerals. You can read more about him here. Also the documentary I mentioned in the other thread is really an excellent production and provides great insight into his life and character, if you can find it online somewhere.

@Andrew M - 'The ENIAC required 30 vacuum tubes to store the decimal 128. Ten for the 1, ten for the 2 and ten for the 8. In addition, it had to turn on 11 tubes.'

No wonder it was so enormous! :yikes:

That top reference hits the nail right on the head. — Wayfarer

:up:

'The ENIAC required 30 vacuum tubes to store the decimal 128. Ten for the 1, ten for the 2 and ten for the 8. In addition, it had to turn on 11 tubes.'

No wonder it was so enormous! :yikes: — Wayfarer

Numbers can be stored in a binary representation about 3 times more efficiently than in a decimal representation (since 2^3 is approximately 10), so 999 (1111100111 in binary) would require 10 vacuum tubes. The miniaturization improvements are really to do with the hardware, e.g., billions of transistors on a chip compared to the space required for vacuum tubes.

they just use Qbits which have three states instead of two (the third state is based on quantum entanglement, so the system is still basically binary). — universeness

A qubit has two measurable states (0 and 1), but a potentially infinite number of superposition states. Entanglement is a different phenomenon and requires two or more qubits.

The miniaturization improvements are really to do with the hardware, e.g., billions of transistors on a chip compared to the space required for vacuum tubes. — Andrew M

Yes I do get that, I learned about moore's law and microprocessing quite some back, but still, the cumbersome nature of the early vacuum-tube models were due at least in part to their processing logic.

I remember reading quite some years ago that a 'musical christmas card' - the type that plays a tinny carol when you open it - contains more computing processing power than existed in the world in 1946.

I remember reading quite some years ago that a 'musical christmas card' - the type that plays a tinny carol when you open it - contains more computing processing power than existed in the world in 1946. — Wayfarer

Reminds me of Marvin, the android from Hitchhiker's Guide to the Galaxy. A brain the size of a planet, and they used him to open doors...

Numbers can be stored in a binary representation about 3 times more efficiently than in a decimal representation ( — Andrew M

Don't you mean more inefficiently? 999 requires 10 tubes in binary, but 3 in decimal. Or do you mean 3 times 10 tubes (10 for each decimal digit)? 8 requires 3 tubes in binary (well, 1-7: 000-111, 8 is 1000), while it needs 8 tubes in decimal? Or is there one tube for 0-9, like one for 0-1? Isn't binary then 5 times as efficient? I mean, if you need 10 tubes for a decimal digit and 2 for a binary, you need 5 times as many tubes. 999 needs 3 tubes though while in binary it needs 10. You need 30 tubes for all decimals 1-999 though and only 10 for the binary version. Is that last to which you refer?

but a potentially infinite number of superposition states — Andrew M

Isn't the number of superimposed states 2^n, where n is the number of electrons entangled?

Numbers can be stored in a binary representation about 3 times more efficiently than in a decimal representation (since 2^3 is approximately 10), so 999 (1111100111 in binary) would require 10 vacuum tubes. The miniaturization improvements are really to do with the hardware, e.g., billions of transistors on a chip compared to the space required for vacuum tubes — Andrew M

Surely using vacuum tubes, switching on or off, to represent decimal, would be a completely different system. You would need to represent 10 states 0-9. In such a system. 999 could be stored using 3 of the 'state 9' tubes. Representing 999 in binary needs 10 tubes. How is 10 tubes more efficient than 3 tubes.
I understand that such decimal representations would not work due to complexity of decimal arithmetic.
The circuitry needed for binary arithmetic is much simpler but I don't see your efficiency argument.

What about:

$\sin (x)\approx x,\text{ }\sin (x)\cong x\text{ }for\text{ }x\approx 0$

or the more mysterious $\operatorname{s}(n)\sim t(n)\text{ for large }n$

???

The latter is the least well-defined symbol. The former means approximately, which of course requires clarity.

You need 30 tubes for all decimals 1-999 though and only 10 for the binary version. Is that last to which you refer? — Cornwell1

Yes - see the ENIAC example link in my initial post (which showed 30 tubes).

but a potentially infinite number of superposition states
— Andrew M

Isn't the number of superimposed states 2^n, where n is the number of electrons entangled? — Cornwell1

I'm referring to the different states that a single qubit can be in. Every point on the surface of the Bloch sphere (where the sphere represents a qubit) is a potential pure state.

999 could be stored using 3 of the 'state 9' tubes. — universeness

Yes, but there are 30 tubes in total, compared to 10 tubes for binary. See the ENIAC example link in my initial post.

I'm referring to the different states that a single qubit can be in. Every point on the surface of the Bloch sphere (where the sphere represents a qubit) is a potential (pure) state. — Andrew M

There are infinite superpositions of spin up and spin down, for one electron. After a measurement the state tends to evolve to a state with both up and down equally present. There are only 2 states involved in the computing. There potentially infinite states, that's true, but you make it sound if this infinity is part of the computing power.

After a measurement the state tends to evolve to a state with both up and down equally present. — Cornwell1

After measurement, the spin state will be definitely up or down, and not in superposition.

There are only 2 states involved in the computing. — Cornwell1

The point of quantum computing is that computation can be done on superposition states. It's just the final measurement that reduces (collapses) to one of the two basis states (0 or 1).

There potentially infinite states, that's true, but you make it sound if this infinity is part of the computing power. — Cornwell1

That wasn't the point of my comment but, sure, I think it's a part of it. Consider modelling nature - the more available states, the more accurately and precisely it can be modelled.

After measurement, the spin state will be definitely up or down, and not in superposition. — Andrew M

Yes, but it not stays in that state, and two states are necessary for quantum computing. There was a computing done in which about 70 (I don't remember the exact number) qubits were involved, facilitating 2exp70 possibilities in parallel.

Had to look these up again to remind me what they represented.
The most advanced maths I taught was Higher and Advanced Higher but I had not taught either for at least 20 years as I was full time Computing after my f9rst 10 years.

≈ : almost equal to
≃ : asymptotically equal to
≅ : approximately equal to

I have never seen these used as operators in computing but I'm sure they are used by some programming language for various purposes.
sin(x) almost equal to x, ok but to start with? does this not depend on which units are used?
sin(90 degrees) = 1 but sin(90) = 0.89399 or am I going in the wrong direction as regards your intended points.

Yes, but there are 30 tubes in total, compared to 10 tubes for binary. See the ENIAC example link in my initial post. — Andrew M

Ah, I see what you mean now!
As the valves became tiny transistors, a decimal system would require 30 transistors to represent the range 0..999 but can such a problem not be overcome using something like floating-point representation? So 999 stored as a 9 vaccum tube and use the 3 vaccum tube to represent the repetition? You would need a method to separate this from storing 93 but....
I think the main reason for not using decimal is still the complexity of decimal arithmetic compared to binary arthmetic.