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Imagine that people discovered a technology that allows executing any algorithm instantly regardless of its complexity.

E.g.

  • Decryption of any encrypted data happens instantly
  • Simulation of systems of any complexity is instant
  • There is no need to have multicore CPUs and GPUs since a single CPU can do all the work in an infinitely small period of time.

Most likely this discovery would lead to global chaos given how humanity trusts cryptographic laws. Let's suppose this technology is affordable by almost anyone and is cheap to use - like Bitcoin, for example.

How would humanity likely leverage that technology?

If anyone knows if what I'm describing has a name, or has been written about elsewhere, that would also be extremely helpful.

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    $\begingroup$ Can one infinitely fast CPU simulate the work of two infinitely fast CPUs? $\endgroup$
    – Alexander
    Commented Mar 23, 2021 at 23:46
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    $\begingroup$ I'm downvoting because questions 2 and 3 don't seem to indicate any thinking has been put into the question, especially three.. "Writings about this kind of breakthrough"? Seriously? At least 2 has some discussion in "Laplace's Demon" with regards to a computer with god-like computing power determinism of the universe, but I don't think even that computer is considered to be infinitely fast. $\endgroup$
    – DKNguyen
    Commented Mar 24, 2021 at 0:06
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    $\begingroup$ Infinite anything tends to break a lot of things - sometimes it can be useful to set a scalar on technology that already exists instead $\endgroup$
    – Greg
    Commented Mar 24, 2021 at 0:08
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    $\begingroup$ Computing power cannot be infinite, because an infinitely fast computer computer consumes an infinite amount of power. (That's because of Herr Professor Doktor Max Planck and his unfortunate discovery that action must always be an integer multiple of a small but finite quantum of 6.62607015E−34 J⋅s , which today we call the Planck constant.) $\endgroup$
    – AlexP
    Commented Mar 24, 2021 at 0:16
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    $\begingroup$ This is open ended question of the form: what if we had infinite X. (time, money, energy, (perpetual) motion, or monkeys at keyboards). The answers are likely to be opinion based. $\endgroup$
    – Gault Drakkor
    Commented Mar 24, 2021 at 0:44

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The destruction of life, the universe, and everything.

Computer operations that are logically irreversible require the production of entropy somewhere else - they have a minimum energy cost. As Bitcoin has taught us, a small network of ransomware transactions requires a small nation's worth of power consumption. Infinite computing means infinite power means infinitely large bang.

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  • $\begingroup$ If our world really is the matrix, then infinity calculation means we finish the simulation instantly and all reality ceases to exist. $\endgroup$
    – DWKraus
    Commented Mar 24, 2021 at 0:11
  • $\begingroup$ @DWKraus not necessarily. More likely, they just pause our simulation, run the other one, and inject the result into ours and presto, no perceived execution time. $\endgroup$
    – Joel Harmon
    Commented Mar 24, 2021 at 0:42
  • $\begingroup$ @Joel Harmon In that case, any entropy cost for the simulation is borne by the real world outside our matrix, and the seeming infinity calculation thing becomes fractionally more plausible. Maybe they have different-enough physics to compensate. $\endgroup$
    – DWKraus
    Commented Mar 24, 2021 at 1:25
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First, welcome to Worldbuilding!

Answering your questions slightly out of order, the technology you describe does not currently exist in a public setting, nor any private setting that has been discussed. So, questions 2 and 3 are unanswerable at this time.

As for question 1, there is a lot we can do with infinite computing power. Assuming the first thing humanity does with the technology is to answer existing questions some options are:

  • Predict the weather with stunning accuracy. Our current weather models are trained on supercomputers and still have some deviation from reality. This technology could allow those models to run in real-time
  • Greatly improve distribution problems. Many tasks involving moving substance X (electricity, packages, water, etc) to destination Y (your home) are fairly complex. Being able to brute-force optimal distribution of these would cut wastes and cost
  • Greatly speed progress in the sciences. AI, physics, and chemistry all come to mind where being able to just have infinite computer power to model the behavior of a system allows for costly but highly accurate methods to be applied all the time.

In the "it is possible but we don't really know how to do it" category we would also have:

  • Predicting the future. Assuming we have some way of storing the data, since the computer can magically process all the data as fast as we can feed it, predicting the behavior of massively complex systems could occur.
  • Perfect mental immortality. Assuming we can figure out how to rig our minds into the metaphorical Matrix, infinite computing would allow infinite perception of time.

Long story short, such a technology would fundamentally change the nature of the world to the degree of the first computer, or potentially even the discovery of fire.

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    $\begingroup$ We can't predict the weather or anything else perfectly without an impossible number of data points. We would just get the usual approximate answer but faster. $\endgroup$
    – chasly - supports Monica
    Commented Mar 24, 2021 at 0:15
  • $\begingroup$ Fair, but one primary difficulty in gathering those data points is the processing time involved to make them useful. One limitation I did not include (but should have) was the storage of the data to feed these algorithms $\endgroup$
    – Greg
    Commented Mar 24, 2021 at 0:20
  • $\begingroup$ Fortunately computing power cannot be infinite, not even in theory... An infinitely fast computer consumes infinite power. So nope, sorry, there cannot be a fast way to brute force AES-256 encryption. $\endgroup$
    – AlexP
    Commented Mar 24, 2021 at 0:23
  • $\begingroup$ Correct - without some changes to our knowledge of physics, "infinitely fast" traditional computing is impossible. That said, there are some interesting theoretical works on quantum computing once you get in the millions of qubits $\endgroup$
    – Greg
    Commented Mar 24, 2021 at 0:26
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Imagine that people discovered a technology that allows executing any algorithm instantly regardless of its complexity.

The nearest we have to this is the universe itself. For all of the estimated 3.28 x 10^80 particles that are estimated to exist, with all their interactions due to relativity, gravity and quantum mechanics, the universe apparently calculates flawlessly where they should all be at every instant.

Decryption of any encrypted data happens instantly

No it doesn't. The data has to be collected and input into your system. This takes time - especially if you are typing it in yourself by hand.

Simulation of systems of any complexity is instant

It might be instant but that doesn't mean it's correct. Take the weather: Are you going to start by putting in the position and direction of every atom? The models we have now depend on measurements at various weather stations. The models will stay the same, you'll just get the wrong (inaccurate) result faster.

There is no need to have multicore CPUs and GPUs since a single CPU can do all the work in an infinitely small period of time.

Well yes, but then Santa Claus can deliver presents all over the world in one night and we only need one of him, so I suppose you are right.

P.S.

Imagine that people discovered a technology that allows executing any algorithm instantly regardless of its complexity.

What about non-terminating algorithms? They take an infinite amount of time to execute.

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Assuming you've done this in an environmentally friendly way, by getting the Matrix to do your calculation for you... Since this allows you to simulate every process perfectly, you have two obstacles remaining to "everything is possible".

First, defining success. If you say "I want to know the laws of nature", you can feed your data into the computer and try every possible set of natural laws to see what works. A little like finding a word with a certain definition in an infinite dictionary, by reading every entry and returning the right one. The challenge comes in expressing what it means for a set of natural laws to match up to reality. Once you've done that, then you can get easy step-by-step instructions to do 'whatever', provided that you can express that.

The comparatively minor obstacle is entropy, which will limit how much you can do ... assuming that current assumptions are valid.

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If we could execute any algorithm instantly or had infinitely fast computers (from the title), we could:

  • Simulate the entire history of every particle of an entire universe over the lifetime of that universe (over 10^97 particles across 200 billion years for ours)
  • For every possible universe (an effectively infinite number) plus every logically impossible universe (also an effectively infinite number)
  • All in parallel at the same time
  • And we could repeat it an arbitrary number of times (despite there being no point in doing so)
  • And perform any type of analysis or synthesis across all the simulation results
  • And still get the full results instantly.

It would effectively be the omniscience of a god. If that's not the answer desired, well, that's what "infinitely fast" implies.

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