Coin flips are wholly independent operations though, aren’t they? The “or” is not provided by the machine.

Coin flips are wholly independent operations though, aren’t they? The “or” is not provided by the machine.

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To me, Time is what separates theoretical logic, which is supposed to be instantaneous from actual logic operations which always happen across time.

Such is the genius and basis behind the work from various folks in the 1930s that led up to digital computing.

Claude Shannon is one but there were several, all approaching a similar notion from different angles: that quantization over time allows logic to be mechanized.

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No, I think it applies here as well. Think of queuing. The coins are fed in serially. Constraints upon the coin movement are:

The hole,
The size and friction of the “glides” it goes down and bounces through,
The fraud detection mechanism and rejection,
until finally it reaches a point where it can be counted serially.

All of that operates across time.

How do I know this? Gravity.

Imagine your coin counting machine in zero-G or several Gs.

It probably would not function properly.

Could it handles coins traveling too quickly or not at all?

Gravity operates over time.

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It’s amazing to consider just how many things MUST go “right” for a logic function to execute properly.

Astounding amount of constraints. An error in any one of them renders errors in the operations.

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Oh, long BEFORE the logic operation.

The single logic operation is a final step in a huge amount of constraints that are required for that SINGLE logic operation to execute and generate expected result.

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Functioning logic operations are perhaps the PINNACLE of human engineering products.

How do you take non-discrete nature and “toothpaste tube” it into perfect little discrete bits?

Ultimate in turning chaos into human constructed order.

From that, we can build things that operate in ways that speed up time.

Constraint down to bits, make them fast and have all of this mini armies going through pipes and switches, and you and I are able to think a thought, type it, and transfer it within milliseconds to each other.

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A continual source of amazement to me is that those bits – EVERY last one of them, is PHYSICAL.

(we can call it “energy” but it’s physical in that it can be measured and constrained to do our bidding with a lot of coaxing and consists of wonky quantas of elections physically going through materials WE manufacture, taking advantage of quirks of nature that occur at such small scales).

How many billiard balls with wonky physics are moving about under my fingers in this laptop?

I couldn’t begin to imagine. It’s probably making more errors than correct operations, causing continual heat from all those thrown out bits (that are physical in nature – tangible and real) – but it’s working.

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wait – not so much errors but resisters that make it hot, although errors in logic operations also do that as the error correction circuits get overworked… but yeah I forgot about resisters for a sec

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NOR gate – check out that resistance! Hot stuff. Now shrink it and print it really tiny for electrons. Super hot stuff. Anything can be built with NOR (parallel) or NAND (serial) — I wonder how NAND is in resistance?

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log46

Ooh – same amount of resistance it seems, although it looks like NAND is simpler with the fewer wires. NAND must be lower energy requirements, lower heat output, cheaper manufacturing cost, I think.

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log45

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It LOOKS like NOR has a bit of memory built into it too as the switch position itself at the bottom has a loop. I bet that loop is memory storage. Gonna find out.

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(I could never read circuits beyond “squiggle is resistor, find where ground is, that’s a switch thing)..

—-

You know more than me. I just muddle through :) Looks like both NAND and NOR can be used for memory: “SR” – Set-Reset. I sort of “knew” this — that is it looks familiar — but I had no active recall of it.

https://www.electronics-tutorials.ws/sequential/seq_1.html

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Oh, but you can build every logical operation using only NAND or only NOR if you wanted.

Apollo computer was constructed solely of 3 input NORs.

AND yes! My intuition on NAND was right: NAND is faster to operate and cheaper to manufacture and takes up less room.

I seem to recall that NAND is more volitile “weaker” over time but can’t remember why.

https://electronics.stackexchange.com/questions/110649/why-is-nand-gate-preferred-over-nor-gate-in-industry

—–

 

Look at this: “logical effort”. I wondered if this existed – a concept like this. Calculating the delay caused by choice of logic. I wonder if our thinking processes went through a similar energy/time efficiency overhaul that we’d think more clearly with less effort? Hm.
 
https://en.wikipedia.org/wiki/Logical_effort
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delay = logical effort * electrical effort + parasitic delay.There’s a deeper truth hiding in that somehow.
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Ah ha! MORE fundamental than NAND or NOR (in silicon) is an CMOS inverter. (complimentary MOS).
 
It doesn’t ask why. It just switches how you ask.
 
But more fundamental than CMOS (in silicon) is MOSFET, which is like having a switch that only turns on without an off mode or only turns off without turning on.
 
But if you put an OFF switch with an ON switch, you get a CMOS.
 
CMOS also does not use any resistors. So it’s almost no waste heat. It also holds its state very well because it changes via VOLTAGE rather than CURRENT.
 
So, you can “set it and forget it”.
 
Realistically it needs a button battery to maintain its state.
 
This is all stuff you probably know and understand already but I’m enjoying through this.
CMOS-Inverter
———-
 https://www.elprocus.com/cmos-working-principle-and-applications/
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I’m so glad that this is “clicking in” now for me – and really glad you’re getting stuff out of it too! Your feedback is encouraging me and talking out loud helps me see to myself if I’m ‘getting it’.
 
I’ll be mulling this over for a while.
 
So I guess to build it:
 
0 -> 1
That’s great. You can turn it on. All 1s. Forever.
 
Now you’re stuck with all 1s. That stinks. But.. what if?
 
1 -> 0
Good. Now you can turn everything off. Forever.
 
Not satisfying.
 
What if?
 
0 -> 1
1 -> 0
 
Good. Now I can choose. Do I want this on? Turn it on. Do I want this off? Turn it off. But…
 
I’m tired of doing all the thinking.
 
What if I could get this to be a little intelligent?
 
That has only 2 parts. Input. Output. 2.
 
But what if I went to 3? Input. Input. Output. 3
 
Now I can do math!
 
0+0 = 1
0+1 = 1
1+0 = 1
1+1 = 0
NAND
 
or:
 
0+0 = 1
0+1 = 0
1+0 = 0
1+1 = 0
NOR
 
From either of those circuits, because they give a only 1  unique answer out of 4 possible combinations, you can build all other binary logic circuits.
 
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 I dunno – is that making sense? I never thought of logic as starting with “on only” and “off only” switches but now that I see that it’s actually how logic circuits are physically manufactured, my mind is more than a little blown.
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