Optical Bench REDUX: Digital Switching can have Analog Functions!

[RJSV]

   What I've indicated, is that, while a partial multiply, like '4 X 7' DOES extend over one column, with the '2' in the result of '28' the point is that the adding up of all the values, from partial multiplies, does not exceed '9' and thus there is no carry propagation caused there.
Worst case, you get a '9' from adding the partials (please also see previous diagram, bottom), so, while you do have to add up the two partials, you can be confident that no carry handler is needed.

[RJSV]

   For management purposes, a project tracking graph displays a couple of goals:

[RJSV]

 In that graph, (last post), a management tool or project tracking for schedules, the first goal looks good, while the other two have promise...albeit a distant one.
   Doing a single decrement is nicely done, although more simply within the bounds of ' normal rounding'.
Perhaps be said as 'analog that closely tries to follow digital form, or step-wise form.

   So, graph shows lower bounds, where there isn't really any functional benefit, or promise of that.
Upper dotted-line bound is where function gets pretty good, maybe ALMOST as good, as something like binary TTL electronics.

[RJSV]

   Lots of speculation on how to get a decent level compare operation.
   Enclosed graph shows typical number squared, with unity point matching...that being '1 X 1' = 1.
   If you've multiplies out, at various points, it nicely separates, where any input above 1 gets increased, (when squared) while inputs lower than '1' get diminished (when any squaring action gets repeated).
Firstly, you could (somehow) use this to separate out, finely, anything even the slightest bit above a '1.0' will get 'blown upwards' to grow large, by way of repeated squaring.
Similarly, any number, just a bit under a '1.0', like '0.93' will also, quickly, move; this time downwards from the '1.0' inflection point.  In both those cases it takes about four iterations, to obtain a '2X' or a '1/2 X' result, from original value being tested.

   Now, having those 'exagerated' values in hand, I would next need to have a 'digitizing' action.  That would turn an extremely large number, like '42', into just a one... a digital '1' to be used as an 'enable'.  So there's that.
On the low side, would want anything less than '1.0' to be (thresholded) to a 'zero', actually difficult to impossible, with these passive optical components.
But, to enable/disable it might be possible to use the parameter (being tested) in an exponent.  That way, instead of AVOIDING some multiply or some addition, conditionally, the optical set-up simply performs the function, thus unconditionally.  Then, adding some very small factor can be almost the same as conditionally doing nothing. (Edit)

   On the high side, of that, any variable that goes ABOVE a '1.0' would, or could potentially, act as an enable by way of setting the exponent (to a '1').

The whole methodology is, as been presented, a 'blind' functional, having no practical 'compare' or 'zero test', (or even explicit PC or program counter).

Passive/Aggressive; I should call it !

[RJSV]

Graph.

[RJSV]

   So the idea is, that even if you can't do a typical test, (for loop ending or finished), like;
   DO WHILE Index>0

   ...you can avoid the testing, directly, but incorporate the variable (loop index in this case) incorporate into some number being manipulated, unconditionally.

   But leaving THAT bugaboo aside, for minute, (and turning back to the diagram of squared number), you can notice that the (starting) values below that '1.0' inflection point will decrease, exponentially, you would get:
   '1/2 squared to 1/4, then 1/4 squared to 1/16...etc',
Noticing that, in my case it would be '0.9' squared to '0.81', then squared to '0.65', then to '0.42'...You can use a rule of thumb, that about 4 operations will get your value reduced by about half.
Now since (I haven't) developer here doesn't have answer for even the basic action of a fully general number by number multiply, there can be a substitute, for general number squaring(!)
Just, simply multiply by '0.9' repeatedly...THAT simple substitute function will ALSO cause an approximate value reduction by one-half.  That's the sort of crude, out of the box thinking required.
Free and loose with the math.

   However, looking at the high end, of the X squared results, those values would not conform to what I want, as the graph, above the '1.0' inflection would not increase, each step, from any substitution of 'X 0.9' over a straight up square, of the value.


At any rate the behaviour I seek can be shown, when starting at '1.05', a number barely above '1.0', when squared gives '1.1', and subsequent '1.21', '1.44', and value '2.07', giving you that doubling effect, every four operations.


   Several missing pieces, but my COMPETITION is hot on my tail...
pretty sure.
--Rick B.

[RJSV]

Oh, and don't forget, this aspect of an optical data BUS is ENCODED, with special offset and ranges.  That being a '4.0' as coded representative, for 'zero' logical.
Your '1.0' logical value being discussed in past few posts, actually will be, physically, at '4.5' being as each integer logical count is size '0.5' realistically.
Since the physical counts are 1/2 sized, then your rounding value, of a one vs. a zero, is at
   '4.25', meaning that anything below '4.25' is considered a logical 'zero'.

   Now, taking this and running with it, I've (intuitively) hit upon a suggestive formula, by way of multiply, by '0.9', a typically seen multiplier, in this thread, but then a 'replacement' or restoration, back to 100% , and that's done by adding back in: a '0.45'.
   This is going to seem cryptic, if lack of explanation, but that '0.45' is from the '4.5', that is the coded version, of a 'one' logical value.
So, if at the inflection point, you do an 'X 0.9' and then put it back by adding '0.45', thus you could say, any input of a 'one logical' will just end up not moving, staying at a 'one'.
   At another number, though, such as (coded) '5', which is representing a logical 'two', then that '0.45' being added back in (after diminishing by X .9), that '0.45' is going to be a bit too low, giving a result of '0.495'.
THAT isn't good, as I seek DIVERGENCE, from inflection, not closer each time.
Similar problem, on lower end, where a coded 'zero' logical, at physical '4.0' or nearby, will be increased, slightly, but again, does not diverge.

   That looks like: '4.0 X 0.9 = 3.6'
        Then '3.6 + .45 = '4.05' so you can see the slight little 'creep', towards inflection at '1.0' (coded at 4.5), rather than the needed 'crawl' downward.  That way, you could get the 2X change, after about four reductions, the needed change that (would have) gotten that value below significance, (and thus you would have had conditional-like action).

"Conditional pseudo functions, CODED analog doing (octal) or near-octal logical...This shiit is making 'blind pseudo-decrements look like a cake-walk.
Competition is heating up, I feel.

[RJSV]

Might be a little sloppy, but happened upon a substitute for general multiplying.  That is, a multiply where it's not one 'permanent' channel or attenuator against a beam amplitude
   Substituting a 2X of factorial gives an excitingly close valued set of numbers,...for instance 7 squared is going to show as '28+28= 56' or 7 too high over 49.

Using input '9', gives '45+45' or 90,...a value a little too high, at 9 above the correct value, '81'.

   For purposes here, it's the divergent properties, but that doesn't stop the use for other, possibly inexact processes.

[RJSV]

Now doing a spot-check, on some multiplies, that aren't squares;
   Trying '5 X 3', you get 5! = 15, with 3!= 6.  So that appears as '21',...at 6 above correct value.   Still not real bad, and possibly correctable.

   Trying '2 X 7', you get '31',...obviously way too far off to be practible.  But most multiplications get closer.
   Trying '7 X 5' gives '43' which isn't far from the correct value of '35'.  Or at least within an order of magnitude.

[RJSV]

Graph shows three curves, doing squares of three starting points:

[RJSV]

(Sorry, that graph needed to go asymptote to zero).

   Graph shows after a few runs, squaring a starting number, you can see; at '1.0', exact, it's unstable but would (continue) producing same new value...if it weren't for a little noise, up or down, in total amplitude.
But starting slightly above an exact '1.0', like at '1.1' will soon go up, approx double, in 3 repeats.
In similar fashion, a start of '0.9' will, after 3 repeats, get you to approx '0.42', or a 1/2 of start.

   Hopefully, a group of repeats can exaggerate this result.  You can see how, after a bunch of repeats, the lower start, of '0.9' will get diminished, more and more.

[RJSV]

   The lower curve, on the squares graph, will go small, fairly quickly, and so it could be used in a conditional test...as a multiplier.     Err; that is, to say my multiplier function don't work, with 2 variables generally.
One of the multiply parameters has to be built-in, structural.

   The other curve, upper curve, takes you nicely upwards, from integer '1.0' but I'm not sure how to get it to saturate, to a consistent form.

Multiply functionality needs a usable, testable decrement, while a COMPLETE decrement functionality needs...a multiply.  That is for doing the squares, in the conditional test.

[RJSV]

Also,...whilst I confessing my sins, that FACTORIAL function mentioned has same flaw / barrier to properly working, having to include a 'counted' addition (same as any multiply would).  That is, any multiply or squaring can be done by way of repeated additions, but still (haven't) solved the methodology for end-of-loop testing (for a zero result).

   As BOSS might say: First try to implement these things (microprocessor instructions), but in absence of progress there, AT LEAST document the effort...That way you can account for time spent (minimal anyway).
You've got a pretty decent estimating decrement, but no real way to test that status.

[RJSV]

Of course, need to update the encoded version, when adding, it's not so simple and primitive, as the (former) physical combining.

   For example, resembling doing any heavy binary math notation, it's just different, some.  Example of doing addition of '3 + 2' where the numbers encoded would now be:
    '4.0 + 3/2' or '5.5' plus '4.0 + 2/2' or '5.0'.
Doing that encoded addition gives result of '10.5' which contains TWO of the base offsets, so subtract a four will give you the answer, encoded with the usual base of '4.0' and at 1/2 scale.  That would be '6.5' result, which is an encoded '5' or the correct answer in uncoded or 'logical' vs physical terms.
   Or, another approach could be to use the answer 'low bits' so to speak; That is if you are using encoded OCTAL, that way can just ignore the upper order, and use the lower 3 bits, encoded.

[RJSV]

   If you take a look at photo, that's a decorative optical fiber 'tree', although I'm not sure if in this case the type of fiber useful in longer distance digital links.   The communication type will have a fiber core that has different refraction index.

   Obviously, predictably, some of the various approaches to passive optical logic (here) have stalled a bit.  Still worth the time (a modest amount).  Lately the problems have revolved around getting suitable video materials, for continued study.

   I'm finding yt videos where approx. 80 % have language and/or basic audio troubles, in comprehending halting language barriers; with a sense that many of these presentations are not taking coherence into account.  I tend to select those yt videos that run for more than 15 minutes, and 'click out' when/if the presentation is, well, continuously indiscernible as to coherence!

   Anyway, some plans are to continue experiments on the bench, using fibers and various optical sensing diodes.

[MK14]

   If you take a look at photo, that's a decorative optical fiber 'tree', although I'm not sure if in this case the type of fiber useful in longer distance digital links.   The communication type will have a fiber core that has different refraction index.

Yes, it would be interesting to know (no sarcasm is either intended or implied here, I'm just illustrating a point), the difference between a circa (I don't know the price, so only guessing), $1 budget set of decorative tree, optical fibres, and a full on research team/company, with a $50 million dollar, annual research budget, and using the latest, high tech (possibly early prototypes, not available for sale, anywhere), optical fibres, of just about the highest available quality, anywhere in the known universe (except dreams and star trek, or similar).

[RJSV]

   I've shown this method before (please see photo).  By snipping off the garden light's LED those two leads, from that little circuit board, can be conveniently plugged straight into a proto board.  Here, I've just simply added in a RED LED from parts bin, but various other items, such as a transistor can utilize the garden light output (from the simple buck circuit).
   That voltage multiplying buck circuit runs at some 220 khz, producing around +3volts for the LED.

   Now, for my purposes that garden light isn't any where near to being switched due to light from a few strands of the fibers (or even the whole bunch), as the intensity is just too low.  But still, I'm curious as to what voltage (changes) happen...A couple of fibers worth of light might only cause an(edit) increase of a couple of micro-Volts.  (edit) That, of course, is measured at the solar cell, nominal 2.5 volts in bright light.
Certainly, that switch arrangement requires a quantity of light you would expect from a full flashlight, rather than a couple strands of fiber, where the flashlight illuminates the whole bunch.
Just curious.

[RJSV]

   Thanks, MK14.
   Previous ventures soaked up about $ 25 k, to obtain a 'real' office setting and start buying needed tools.  But those are single instance expenses, office rent ongoing but not very much ($220).
Ongoing, beyond initial seed money, was rent and labor time...lots and lots of labor time.  I took on a job, when it was offered, so that helped with paying the office rent.  Overall, was 5+ years with some productive outcome...(mostly gained wisdom), and better appreciation for US Patent Office procedures...

[RJSV]

   Now, since I'm going to be trying out a single, extremely feeble portion of total light, via one isolated strand of that (decorative tree), I started on kitchen table, getting a rough count, (of total fibers there).

   The bundle diameter is close to 9/16 inch, where the area calculates to, est. π/12.6 sq inches (roughly 1/4).
The fiber 'gauge', lacking a handy micrometer, was then estimated: 20 fibers side by side takes up 11/32 ". comes to est. 17.6 thousandths of inch.  So, I used 20 here, Fibers est. at 20 thousandths diameter.

   Run that out, total area divided by area of a single fiber (fiber is est. π\ 10,000); that divides to 10,000/12 or about 833 fibers !

   (Wow, lucky, that's a 'magic' number...or at least 0.833 is...    That's 6/7ths).

   Anyway, if you figure around 1000 fibers, or 833, that's the factor of reduction.  So, if a 10 milliwatt LED manages to shine about 4 mW directed into that bundle, you 'could' expect around 4 MICROwatts at the end of exactly one fiber, separated and isolated by dark cloth. 
   That also would apply, approximately, to say a viewer's perception, each of the tiny tiny points seem almost to be less intense,...than the stars, individually seen, at night.  Wow.

These preliminary estimates are to be checked and measured next, on the bench.

[RJSV]

   Measuring voltage response, using solar cell as sensor, like the garden light's do;
   With minor light leaks, through cloth, the little solar cell reads 0.030 (30 milliVolts), and then with 'signal' we read 0.520 volts, approx. which is the response I'm looking to measure, while using small bundle.
Small fiber bundle is approx. 1/16 of area of full, 1000 strands, or about 62 fibers, at 250 microWatts total.
If that's correct, it's close to 4 microWatts estimated, per fiber.  (That's when assuming 4 milliwatts goes into the whole, 1000 fiber bundle.)

[RJSV]

Please forgive, some of these preliminary numbers aren't trustworthy yet.
   Paring down to FIVE individual fibers, out of the 1000 fiber bundle, I've gotten it to go through change of 0.008 volts (8 milliVolts), dark, changing to 0.030 (30 millivolts), illuminated, with 5 strands.

   However, I need to solidify things, on the table here, as my light baffle has to securely hold the 5 little optical fibers, while simultaneously blocking and holding the rest of the bundle secure.
But, it looks like the electronic aspects, of detecting that little portion of light is easy, if feeble.  Need to set up to read that photocell current as well, but seems a sensitive FET can easily handle the (30 mV), even if total power isn't much.
Tomorrow, better test jig...

[RJSV]

   Wanted to briefly show, an older concept, of using the lawn lights as digital switches, having less layout rules, as it's light beam paths that carry signals, where usual electronics has...wirrs.
(That's broken slang, for 'Wires').
I noticed right away, that such 'amorphous' gate interplay was causing a latching ability, similar to cross-connected gates.

[RJSV]

(Electronics would simply run traces wherever needed, regardless of any requirement (in optical) for running 'straight line' signal paths.

[RJSV]

So also, while viewing the last two Garden Light layout arrangements it should be clarified that the 'two' inputs featured, in the NOR gate illustrations, the meaning is really 'one or more' inputs, depending on where each light beam is traveling.  Two inputs shows, how the little gates can be used as '2 input NOR' logic.
In an 'accidental' bio-system layout, that random orientation would be, could be, massive numbers, like hundreds of tiny cells, waiting for evolutionary selection to act.  Eventually, a complex system could emerge, from the disorganized jumble presented here.

The latter diagram shows a nicely reorganized and more clearly discernable structure...implementing classic 'SR' FlipFlop.

[RJSV]

Maybe not obvious, but in context of popular neuro-network analog qualities, you would have attenuation (i.e. adjusting analog input weights), caused or controlled through device spacing and optical beam angles.
Of course this sort of free-space in 3-D layout wouldn't be used in some of the integrated devices...they used optical fibers and conduits, waveguides, rather than free space setups.