Computer engineer Eric Holloway tells us the story of a king who was offered just such a machine:

Once upon a time, there was a king who loved feats of engineering. He had everything he could want: his own supercomputer, an invention cave with an assortment of ingenious robots and vehicles, and a mechanized, sensorized castle that could reconfigure itself at his slightest whim. For protection, he had a gigantic laser beam to fend off invading hordes, from his own planet or from outer space. However, the king was not satisfied. There never seemed to be enough new-fangled devices for him to try.One day the inventor Schmedrik came to visit the king. “I have what you need,” said Schmedrik, “The only thing that can satisfy your need for new inventions is a perpetual invention machine. And I have just such a machine for you, the Innovator, for the low, low price of one quintillion bitcoin.

“Well yes, that may seem at first like a large sum. But considering that all the inventions will be worth something and that this machine creates an infinite number of them, any finite fee I charge you is a bargain.”

The king was pleased with Schmedrik’s proposal. But just as he was about to hand over the requested amount, his wise advisor Previsio pulled him aside and whispered, “Dear king, before we pay Schmedrik his fee, do you not think it prudent to first determine if the Innovator works?”

Eric Holloway, “Could one single machine invent everything?” atMind Matters Today

Ah yes, does it work? *Can* it work?

*See also:* Why evolution can never get any smarter (Basener’s Ceiling)

Fisher’s proof of Darwinism flipped: William Basener replies to Erasmus Wiffball

and

Who creates information in a market? Johnny Bartlett: Do exchange-traded funds (ETF) make personally gathering information obsolete? Algorithmic strategies can only be as good as their informational inputs. Ignoring the informational inputs to algorithmic strategies causes us to misunderstand the dynamics of value creation in any system. Algorithms can leverage information, they can’t create it.

FTA:

“Yet, here we have a situation where an angelic recipe of 100 lines has created something that has an angelic recipe of 1000 lines. That, my friends, is a contradiction.”

But it’s not a deterministic recipe, it’s a recipe plus randomness. I.e., a computer program that randomly extends itself and then tries out the result. After an impractically large number of tries, it could stumble onto a larger, but still minimal program for doing something new. Not sure I see why the article’s argument succeeds.

(Again, not workable with atoms etc., due to time constraints. So materialistic evolution still has no chance. I’m just analyzing the argument…)

@EDTA The Innovator guarantees *every* invention is unique and fantastic. The random stumbler does not have that property.

Ah yes, the Random Stumbler^TM is the Innovator^TM’s main competitor in the market, right? It is often bought and installed by politicians on the theory that they will eventually do something right.

As for the track record, well, this is not a political blog… 😉

@EDTA Another way one could take your argument is the Stumbler eventually stumbles on a new invention, and then and only then generates it for the satisfaction of the king. However, the selector which filters out only the good inventions results in the same problem. Since it guarantees only good inventions, there is a limit to how many good inventions it can produce.

To expand on the above point, let’s say we had a purely random stumbler who is bound to stumble over every possible invention sooner or later.

The Maximal Satisfaction Filter will only select the best of these inventions.

Now, this filter has an angelic recipe.

Additionally, we can add one more step to the recipe that tries out every invention one by one in a rule based manner, instead of randomly.

This rule based filter is equivalent to the random stumbler + filter, yet has no randomness and reduces to an angelic recipe.

So, we see it has the same basic problem as the Innovator.

So basically the King wants a “perpetual invention machine” but a “perpetual invention machine” is impossible since it violates the “Law of Conservation of Information”.

Along that line of thought it is interesting to note that “inventions” are, basically, the infusion of information into material substrates in new, interesting, and useful ways.

And although man’s ability to infuse information into material substrates was rather crude to begin with, over the last half century or so this ability of man to infuse information into material substrates has grown more and more sophisticated and precise.

As Peter Tyson stated in the following article, “Indeed, many of the technologies you and I enjoy every day simply would not work without mathematics. When you do a Google search, you’re relying on 19th-century algebra, on which the search engine’s algorithms are based. When you watch a movie, you may well be seeing mountains and other natural features that, while appearing as real as rock, arise entirely from mathematical models. When you play your iPod, you’re hearing a mathematical recreation of music that is stored digitally; your cell phone does the same in real time.

“When you listen to a mobile phone, you’re not actually hearing the voice of the person speaking,” Devlin told me. “You’re hearing a mathematical recreation of that voice. That voice is reduced to mathematics.”

Might I also suggest that since “an infinite number of true mathematical theorems exist that cannot be proved from any finite system of axioms”

and since the most interesting inventions that are being invented now are basically using mathematical, algorithmic, information,,, then the number of ways in which man can infuse information into material substrates in new, interesting, and useful ways in order to create new inventions is potentially limitless.

For all the would be Thomas Edisons out there hoping to find the ‘next big thing’, might I also suggest that the criteria of beauty would be extremely useful to you in your search for a ‘new’ mathematical theorem to possibly infuse into a material substrate in a new way in order to create a new, interesting, invention?

Of related interest to theoretical mathematics that are fruitful to the progress of science (and inventions), it is said that the best mathematical theories, that are later confirmed empirically to be true, were born out of the mathematicians ‘sense of beauty’. Paul Dirac is said to have mathematically discovered the ‘anti-electron’, before it was empirically confirmed, through his mathematical ‘sense of beauty’:

As the preceding video highlighted, Paul Dirac was rather adamant that beauty was integral to finding truth through math and even went so far to state that,,,

Also of note

Of supplemental note: The ‘argument from beauty’ is a Theistic argument:

You are correct BA77, and thanks for the interesting articles. You have quite the amazing personal index of resources. Incidentally, the academic paper I wrote uses Chaitin’s incompleteness theorem.

In lines with what you wrote, here is a proof that chance + algorithms cannot create mutual information with mathematical truth:

https://core.ac.uk/download/pdf/82092683.pdf

The law goes by various names, here it is called the “law of independence conservation”.

EricMH, if you could break that “law of independence conservation” down a bit, please.

Exactly what independence of exactly what entity, over and above information, is being conserved?

What we call “information” is technically known as “mutual information”. It is how much thing A reduces our uncertainty about thing B. Stated another way, it is how much information A gives us about B.

If H(B) is the amount of uncertainty regarding B, then H(B|A) is how much A reduces uncertainty about B. So, we measure mutual information by:

I(A;B) = H(B) – H(B|A).

The law states that if you apply an algorithm f(A), which can also have randomness added, it cannot not increase I(A;B) beyond any information already in f.

I(f(A);B) <= I(A,f;B).

In other words, there is no way to get more mutual information than you started with.

Doh, double negative!

“it cannot not” should be “it cannot”.

Perils of editing strike again.