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Application of computer with invertible arithmetic?

Started by DonGateley 5 years ago16 replieslatest reply 5 years ago96 views

I've put together a computing system in which all arithmetic is perfectly invertable. (Will appear as a Node.js application.) The inputs are as determined by the outputs as the inputs determine the outputs. This implies that all linear transform or linear transform chains are also inherently revertible to any point of the calculation.

My application for this is to try to build a computer that directly implements the QBist interpretation of quantum mechanics but it occurred to me that there might be application in DSP for a compute engine with this property. While invertibility is a requirement of a QBism system it seems to me it might have broader (narrower?) application.

If anybody has ideas for such applications, I would love to hear about them. I would think that adaptive linear processes could benefit greatly from an intrinsic back-up operator to try again with different assumptions from arbitrary points in the process. 

One can devise special forward linear transform algorithms without the need to specify any inverse algorithm. Or the other way around.

etc.


Bob Cain

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Reply by drmikeJuly 24, 2016

For everyone wondering what the hell he is talking about, check this out:

http://arxiv.org/pdf/1311.5253.pdf


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Reply by DonGateleyJuly 24, 2016

Thanks, that is what provided me the motivation to start looking at QBism but is actually of little relevance to the question. I'm hoping to see a narrower discussion of the utility of self reversible transformations to DSP. If any.

Is RBJ still around these parts? I'd love to hear from him.

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Reply by stephanebJuly 25, 2016

Let me ping @rbj for you in case he would like to contribute to the discussion. (all you have to do, assuming you know the username of the person, is to add an '@' before the username..)

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Reply by DonGateleyJuly 25, 2016

Thanks, Stephan(e).

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Reply by rbjJuly 25, 2016

well, i never much hung around these specific parts.  this might be my very first DSPrelated post.

i remember Bob Cain from the comp.dsp daze.  if i remember right, Bob had a few scraps with some other goofy english dude (that Gareth guy).


i clicked that link and it's about quantum mechanics.  what is a Qbist?


am i missing something obvious?

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Reply by DonGateleyJuly 25, 2016

Yeah, same Bob Cain. It was Gary Sokoloich. He began watching for anything to appear by me anywhere on the internet and responding with his joyous personal attacks. I think you had some run-ins with him too. I guess I hit him a little too close to home.

You and I had an ongoing adversarial conversation on interpreting the Fourier transform and its so called periodicity. It remained friendly, though.

Actually, I never should have mentioned QBism despite it being the cause of my work. It is a fascinating topic but not one particularly relevant here.

One of the things that came out of my recent work was an arithmetic system that is invertible. If you know the outputs of an arithmetic operation, you can determine the inputs. You can stepwise reverse chains of linear operations as easily as a single one.

It occurred to me that this property might be useful in signal processing and want to explore what those uses might be with anyone willing to think about it. I figured that among this august group there might be such a thinker or two and hoped for you as one of them.

Back to QBism for a second, I've architected and am implementing a compute platform that implements, among other things, the QBist paradigm. Turns out it is far more useful as a general purpose operating system with some amazing properties, I call it UOS for Universe Operating System and am in process of defining and coding it in Javascript (Node.js) One need know or care nothing at all about quantum mechanics to utilize it for daily computing and data processing but if one wants to reach that level of understanding it can simulate a quantum event and whole universes of them with extreme accuracy.

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Reply by rbjJuly 25, 2016

yeah, it was Sokolich (who was around the alt.sci.physics.acoustics newsgroup when it was active) not the goofy brit named Gareth.

didn't remember that i was scraping with you about the **Discrete** Fourier Transform and it's "so-called" periodicity.  (the continuous Fourier Transform is not inherently periodic, but the DFT is.) i was scraping with a lot of people about that.

well, unless you're carrying some metadata around with your data, i dunno how you can invert an operation that has two inputs and one output.

like the sum of x+y is 15.  what is x?  if you can answer that without metadata attached to the sum (like the difference between x and y), then i would say you have beaten Shannon.

still have no idea how Quantum Mechanics has anything to do with Operating Systems.  (i have a notion of how someday one might make a gate at that level.  and it would be a "fuzzy" gate.)


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Reply by DonGateleyJuly 28, 2016

Sorry, Robert. I was suddenly taken ill. Not yet recovered and will get back to this when the daze clears.

First thing I've got to decide is whether what I posted was from delerium or whether it was real. :-)

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Reply by shafie7July 24, 2016

Hello Bob,

What do you mean when you say "special forward linear transform algorithms without the need to specify any inverse algorithm"?

Does that imply knowing FFT, you can compute IFFT and vice versa?

If so, this potentially have other applications and we should talk further.

Best regards,

Shahram

ortenga.com

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Reply by DonGateleyJuly 24, 2016

Yes, exactly. Or any other stepwise linear transform. Please talk further. :-)

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Reply by shafie7July 24, 2016

There are applications in Wireless Communications.

Please let me know via email, if you would like to follow up with a video call forum to explore more.

My consulting firm, ORTENGA, can help you find an appropriate application(s) for it.

Best regards,

Shahram

ortenga.com

shafie@ieee.org

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Reply by DonGateleyJuly 25, 2016

Thanks, Shahram. My implementation of this is incomplete although the characteristics stated are assured. I won't be making any of the type of contact you are proposing until I can demonstrate it. If there is a possibility of exploiting it to bring some comfort to my retirement (I didn't do awfully well at that) you can be sure I'll be exploring that above all. :-)

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Reply by shafie7July 25, 2016

5G technology will require more efficient yet robust data handling.  The 5G technology is in process of standarization, and if this new algorithm is any more efficient/implementable than existing one, then you may be onto something worthwhile and would benefit you more than your previous experiences.

Best regards,

Shahram

shafie@ieee.org

ortenga.com

forum5g.com

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Reply by DonGateleyJuly 25, 2016

It will take very special hardware to make this computationally advantageous. I have designed such hardware myself that performs the basic arithmetic operations in a single cycle and see that it can also be very efficiently implemented on GPU's.

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Reply by shafie7July 25, 2016
Application Specific Integrated Circuits, ASIC, can be designed if the algorithm is robust and efficient.  Nowadays ASIC consists of billions of gates with GHz speed in couple of mm^2 area.
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Reply by DonGateleyJuly 25, 2016

Thanks, I will look into that as a platform. Got a link to an outfit that could do the fab and provide DIY design tools that don't require a Ph.D? Maybe even provide a free line slot to get one made. It's a lot bigger than your average ALU but not ridiculous. Well, maybe even ridiculous but not absurd. :-)