Berry's Paradox - An Algorithm For Truth

What is a number that can't be expressed in a binary number system?

Very annoying that closed captions turn on by themselves

Rayos number is the smallest biggest number check it out its pretty close to what you describe

This "feels" pretty much like Gödel's incompleteness theorem or the halting problem. Maybe with enough "abstraction" (e.g. category theory?), we can see that all of such negative results are basically the same.

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Occam's Razor is best expressed in words as "an explanation must be as complex as is necessary to explain a given phenomenon, but not any more complex than that." In other words, it's not "the simplest idea is the best" but rather "the idea that has no unnecessary elaborations or assumptions is most likely to be the best description of how the phenomenon is generated."

"You can't describe all numbers, so it logically follows that there must be a biggest number you can describe." - This isn't true; imagine you could describe even numbers but not odd numbers - there's neither a largest number you can describe nor a largest number you can't describe.

on is the biggest number. on, defined as {on|} is greater than all other reals, all other surreals, and all other combinatorial games, except those which it is confused with.

i thought of ∞

my description of ∞ is "it's a number that goes on forever"

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This is a fantastic read. It reminds me of a book with similar content that altered my life’s trajectory. "Game Theory and the Pursuit of Algorithmic Fairness" by Jack Frostwell

"Size" of a number is already an assumption.

Uhm the world was created 2023 years ago so there is not a number larger than that smh

The problem is.... if some value (a sequence of zeros and ones) matches the Sun's activity does it mean that this sequence can be described by three words ("the Sun's activity")?
If some string is the same as some another random string in the past then is it describable by that string or not? :)
And is it even fair to use our universe as a source of ideas to identify the minimal length of description for something? Think a universe where Pi is equal to 4.6787234823423.... because their universe is curved in some specific way so every measurement of Pi gives that value. Is it right to say that 4.6787234823423... can be described with two letters "Pi"? And for example should we think a division (a/b) as one operation or as 80 operations (or how much it takes in a computer processor, I don't remember the number)?
Until we have a definition for "information" we can not measure information at all :)

my biggest number is φ,(φ(φ(φ(φ(φ(.....))))))

I dont care. Tom Scott said there's none, so there's none!

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I believe that Occam's Razor is actually a misspelling of Occam's Rasoir.
rasoir comes from the French verb meaning 'to reason.'
In truth, Occam's Razor means Occam's reasoning, and doesn't have very much to do with the careful removal of unsightly female facial hair. Of course, I might be mistaken.

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The first example reminded me of a Turing machine and the halting problem kind of

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The biggest number I can think of is 7. Prove me wrong.

If Solomonoff had succeeded, he would have solved the notorious problem of induction. Unfortunately, he failed. We may stumble on the truth, but we can never prove that we have actually found it.

Simply fantastic..

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I'm curious what would happen if program running time and memory usage were to be limited. I bet there would be no paradox, it would be all computable.

Numbers represent positions of quantity, which is when you can divide something into equivalent parts.

Great video, but so disappointing to see the popular misstatement of Occam's Razor.

42 is the answer ;)

isnt using pi=C/d to derive pi a form of circular reasoning?
because you can not know the exact value of C (an irrational number) without knowing pi
pi is irrational as well so its numbers have no pattern

Mathematics is a model of reality, not reality. There may inconsistancies.

every number because saying "undescribable number" in itself is a description

maybe that mean that "FindShortestString" is actually not shortest and version2 of it will be program that is combined from "FindShortestString_v1" + "Berry's Paradox". and it will be "true" FindShortestString then

I don’t understand the arbitrary assigning of 100 and 40 bits size to the theoretical programs at the end of the video. What does the ratio of these programs’ size to one another have to do with the input or output?

that poor lady was counting in her sleep

How would the description "most transcendental numbers" relate to Berry's paradox? Yes, it describes an (uncountably) infinite class of numbers, but it is a very concise description, and I can't help but wonder...

The rock paper scissors site is interesting in its simplicity. According to the people behind it, it just sees what you're most likely to pick based on your favourite play. Basically like rolling a weighted three sided die with the weight decided by your frequency

Infinity - 1 = Just way before infinity