All the Numbers - Numberphile
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Date: 2022-04-09
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Comments and reviews: 9
jojojorisjhjosef
When thinking about physics it makes sense we have known unknowns like dark matter/energy, we did some measurements but we don't have an underlying theory. But when thinking about Maths (or rather logic) having known unknowns is just super weird, weird on the level of paradoxes, how can we build up logic up to a point at which we know that we won't know them? Not like an unanswered question, a question that won't ever be answered (unlike in physics.
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When thinking about physics it makes sense we have known unknowns like dark matter/energy, we did some measurements but we don't have an underlying theory. But when thinking about Maths (or rather logic) having known unknowns is just super weird, weird on the level of paradoxes, how can we build up logic up to a point at which we know that we won't know them? Not like an unanswered question, a question that won't ever be answered (unlike in physics.
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Eye
Does the definition of a normal number not specify that it must contain any finite string? Otherwise, one could ask for the normal number to contain the normal number that it is without the decimal, making it a repeating number and incapable of containing anything else infinite. This has got to have been accounted for. I refuse to believe that I, an Algebra 2 student, could find such a large issue in mathematics.
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Does the definition of a normal number not specify that it must contain any finite string? Otherwise, one could ask for the normal number to contain the normal number that it is without the decimal, making it a repeating number and incapable of containing anything else infinite. This has got to have been accounted for. I refuse to believe that I, an Algebra 2 student, could find such a large issue in mathematics.
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Celia
If computers can generate random numbers doesn't that make them all computable? I suppose it's limited by how many decimal places you can go to.
Perhaps it would be interesting to look at irrational numbers like pi, e, square root of 2 or 3 etc, golden ratio, logs of numbers to various bases. in binary or hexadecimal or any other base! Is there a video on these?
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If computers can generate random numbers doesn't that make them all computable? I suppose it's limited by how many decimal places you can go to.
Perhaps it would be interesting to look at irrational numbers like pi, e, square root of 2 or 3 etc, golden ratio, logs of numbers to various bases. in binary or hexadecimal or any other base! Is there a video on these?
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Chlorate
Oo here's one, if you were to have a magic set of calipers that could measure something with infinite accuracy and used it to measure something it would give you an uncomputable number.
I say magic because in the real world although there is no such thing as exact, there is a fundamental limit to how small a thing can be measured before physics stops working.
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Oo here's one, if you were to have a magic set of calipers that could measure something with infinite accuracy and used it to measure something it would give you an uncomputable number.
I say magic because in the real world although there is no such thing as exact, there is a fundamental limit to how small a thing can be measured before physics stops working.
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Subduralempyema
Could have also added definable numbers: numbers that can be defined in a formal language (so any number you can in any way define uniquely. These numbers form a countable infinity (as all formal sentences are finite strings of a finite set of symbols, so almost all numbers are undefinable, i. e. such that you cannot even specify any one of them.
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Could have also added definable numbers: numbers that can be defined in a formal language (so any number you can in any way define uniquely. These numbers form a countable infinity (as all formal sentences are finite strings of a finite set of symbols, so almost all numbers are undefinable, i. e. such that you cannot even specify any one of them.
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Matthias
Still my most beloved Numberphile video. I've watched it so many times now, it flashes me every single time.
Whenever I feel tempted to believe that we may have maths figured out for the most part, I watch this video. And bam, I'm back at square zero.
Really an intellectual shower if you think about it, for getting rid of primate-brain hubris.
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Still my most beloved Numberphile video. I've watched it so many times now, it flashes me every single time.
Whenever I feel tempted to believe that we may have maths figured out for the most part, I watch this video. And bam, I'm back at square zero.
Really an intellectual shower if you think about it, for getting rid of primate-brain hubris.
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Xerxes
no, that doesn't make sense. take any normal number and remove a digit sequence, say 13456789101113etc (remove any 12) and you have one number that isn't a normal number. now repeat this for all finite sequences of digits, and you have infinitely many non-normal numbers per normal number. Normal numbers can't be most numbers. (corrections welcome)
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no, that doesn't make sense. take any normal number and remove a digit sequence, say 13456789101113etc (remove any 12) and you have one number that isn't a normal number. now repeat this for all finite sequences of digits, and you have infinitely many non-normal numbers per normal number. Normal numbers can't be most numbers. (corrections welcome)
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Travel
Watching this always makes me think vaguely of H. P. Lovecraft, and the notion that the universe that we live in and understand is just a tiny little infinitesimal blip and beyond lies a vast, unknowable universe of entities that cannot be described (They would drive you mad. And yet. somehow. they are not terrified when thought of this way.
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Watching this always makes me think vaguely of H. P. Lovecraft, and the notion that the universe that we live in and understand is just a tiny little infinitesimal blip and beyond lies a vast, unknowable universe of entities that cannot be described (They would drive you mad. And yet. somehow. they are not terrified when thought of this way.
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Rainer
It is -not- obvious that Champernowne's constant is normal. Your definition of normal numbers is a bit sloppy. Every string of digits has to appear infinitely often and all strings of the same length with the same -probability- (asymptotic density. To prove this is true for Champernowne's number took 6 pages in his paper published in 1933.
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It is -not- obvious that Champernowne's constant is normal. Your definition of normal numbers is a bit sloppy. Every string of digits has to appear infinitely often and all strings of the same length with the same -probability- (asymptotic density. To prove this is true for Champernowne's number took 6 pages in his paper published in 1933.
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