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How to fit any dataset with a single parameter

arxiv.org

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Re: How to fit any dataset with a single parameter

#31

Post by KerrickStaley »

cs702 wrote: post #23

Fun read. But if we allow ourselves as much precision as we need, we don't even need a parameter. Any constant that is a normal number should suffice. Such constants already contain every possible sequence of digits you could muster -- i.e., they already contain every possible dataset. EDIT: I replaced "transcendental" with "normal" after reading Scarblac's comment below: https://news.ycombinator.com/item?id=28699622…

It's not true that any transcendental number would work. A transcendental number is a number which isn't the root of any polynomial with rational coefficients. This property doesn't imply that it contains all number sequences.

It hasn't even been proven that pi contains all number sequences.

See https://math.stackexchange.com/questions/216343/does-pi-cont... for more details.

Re: How to fit any dataset with a single parameter

#32

Post by wallacoloo »

mjburgess wrote: post #22
air7 wrote: post #17

This reminds me of a joke idea I read somewhere: You can encode the entire Encyclopaedia Britannica using a single mark on a simple stick! Just encode the text as a ascii codes after the decimal dot of a zero. (0.656168.. etc). Then just mark that ratio of the sticks length and you're done...

I don't see this as a joke, but a radical and important point. Reality, in being geometrical, is infinitely informationally dense (with a discrete conception of information). This distinction between geometrical space and time, and discrete algorithmic computability is unbridgeable. And hence there is an extemely firm footing on which to reject: AI, brain scanning readers, teleporters, etc and most sci-fi computation…

These are weird conclusions. Any attempt to measure “reality” gives some amount of uncertainty. The only way for this to lead to the relatively stable experience you perceive is if those small variations in measurement lead to relatively small differences in perception. In which case, you can truncate the resolution of your simulation and still get plausible results.

I assure you there are plenty of groups out there simulating systems that operate with similar densities (but lower volume) to the brain.

Re: How to fit any dataset with a single parameter

#33

Post by _2d30 »

cs702 wrote: post #23

Fun read. But if we allow ourselves as much precision as we need, we don't even need a parameter. Any constant that is a normal number should suffice. Such constants already contain every possible sequence of digits you could muster -- i.e., they already contain every possible dataset. EDIT: I replaced "transcendental" with "normal" after reading Scarblac's comment below: https://news.ycombinator.com/item?id=28699622…

This actually isn't known to be true afaict: https://www.askamathematician.com/2009/11/since-pi-is-infini...

Re: How to fit any dataset with a single parameter

#34

Post by cs702 »

Scarblac wrote: post #27
cs702 wrote: post #23

Fun read. But if we allow ourselves as much precision as we need, we don't even need a parameter. Any constant that is a normal number should suffice. Such constants already contain every possible sequence of digits you could muster -- i.e., they already contain every possible dataset. EDIT: I replaced "transcendental" with "normal" after reading Scarblac's comment below: https://news.ycombinator.com/item?id=28699622…

I don't believe just being transcendental is sufficient for that property. E.g. I can't imagine that pi with all the '1' digits replaced by '2' isn't transcendental, but it clearly doesn't contain every sequence of digits. I think you mean normal numbers.

You're right: normal, not transcendental.

IIRC, most real numbers are normal, and many important transcendental numbers are thought to be (but have not been proven to be) normal.

I edited my comment. Thank you for the correction!

Re: How to fit any dataset with a single parameter

#35

Post by mgraczyk »

mjburgess wrote: post #22
air7 wrote: post #17

This reminds me of a joke idea I read somewhere: You can encode the entire Encyclopaedia Britannica using a single mark on a simple stick! Just encode the text as a ascii codes after the decimal dot of a zero. (0.656168.. etc). Then just mark that ratio of the sticks length and you're done...

I don't see this as a joke, but a radical and important point. Reality, in being geometrical, is infinitely informationally dense (with a discrete conception of information). This distinction between geometrical space and time, and discrete algorithmic computability is unbridgeable. And hence there is an extemely firm footing on which to reject: AI, brain scanning readers, teleporters, etc and most sci-fi computation…

I wouldn't say that the distinction is "unbridgeable". Keep in mind that we send packets over plenty of "geometrical" and seemingly infinitely dense analog channels all the time, like electricity over a copper wire or EM waves over the air.

The "mark on a stick" channel has a capacity like any other channel. If you're sending just one symbol, you could easily calculate the information capacity given a desired probability of bit-error.

Assuming you can put the mark in exactly the right spot, you can model the "noise" as a distribution over the values that the reader will measure. If you model this as `mark + zero-mean normal distribution` with a known variance, then your stick is just an AWGN channel.

Re: How to fit any dataset with a single parameter

#36

Post by Rapzid »

idiotsecant wrote: post #25
mjburgess wrote: post #22

Earlier quoted context omitted.

I don't see this as a joke, but a radical and important point. Reality, in being geometrical, is infinitely informationally dense (with a discrete conception of information). This distinction between geometrical space and time, and discrete algorithmic computability is unbridgeable. And hence there is an extemely firm footing on which to reject: AI, brain scanning readers, teleporters, etc and most sci-fi computation…

Reality isn't quite infinitely dense though, it's hard to imagine how you could encode data geometrically over a distance smaller than the planck length, for example. Reality just has a very, very fine resolution.

A quick Google shows 6.25e+34 plank lengths in a meter. So, seems impossible to measure and make the mark.

Edit: As a fraction of appended ascii codes.

Re: How to fit any dataset with a single parameter

#37

Post by dlivingston »

mjburgess wrote: post #22
air7 wrote: post #17

This reminds me of a joke idea I read somewhere: You can encode the entire Encyclopaedia Britannica using a single mark on a simple stick! Just encode the text as a ascii codes after the decimal dot of a zero. (0.656168.. etc). Then just mark that ratio of the sticks length and you're done...

I don't see this as a joke, but a radical and important point. Reality, in being geometrical, is infinitely informationally dense (with a discrete conception of information). This distinction between geometrical space and time, and discrete algorithmic computability is unbridgeable. And hence there is an extemely firm footing on which to reject: AI, brain scanning readers, teleporters, etc and most sci-fi computation…

Even if space and time were continuous (which things like the Planck length would discredit), there are still discrete objects in that continuum.

Elementary particles, for example, are discrete. You could argue that they have continuous effects vis a vis the EM field and spatial positioning, but ensemble effects usually render that irrelevant at large enough scales.

Re: How to fit any dataset with a single parameter

#38

Post by cs702 »

_2d30 wrote: post #33
cs702 wrote: post #23

Fun read. But if we allow ourselves as much precision as we need, we don't even need a parameter. Any constant that is a normal number should suffice. Such constants already contain every possible sequence of digits you could muster -- i.e., they already contain every possible dataset. EDIT: I replaced "transcendental" with "normal" after reading Scarblac's comment below: https://news.ycombinator.com/item?id=28699622…

This actually isn't known to be true afaict: https://www.askamathematician.com/2009/11/since-pi-is-infini...

You're right. I edited my comment. Thank you for pointing it out!

Re: How to fit any dataset with a single parameter

#39

Post by cs702 »

KerrickStaley wrote: post #31
cs702 wrote: post #23

Fun read. But if we allow ourselves as much precision as we need, we don't even need a parameter. Any constant that is a normal number should suffice. Such constants already contain every possible sequence of digits you could muster -- i.e., they already contain every possible dataset. EDIT: I replaced "transcendental" with "normal" after reading Scarblac's comment below: https://news.ycombinator.com/item?id=28699622…

It's not true that any transcendental number would work. A transcendental number is a number which isn't the root of any polynomial with rational coefficients. This property doesn't imply that it contains all number sequences. It hasn't even been proven that pi contains all number sequences. See https://math.stackexchange.com/questions/216343/does-pi-cont... for more details.

You're right. I edited my comment. Thank you for pointing it out!

Re: How to fit any dataset with a single parameter

#40

Post by an1sotropy »

air7 wrote: post #17

This reminds me of a joke idea I read somewhere: You can encode the entire Encyclopaedia Britannica using a single mark on a simple stick! Just encode the text as a ascii codes after the decimal dot of a zero. (0.656168.. etc). Then just mark that ratio of the sticks length and you're done...

I remember reading about this as a kid in one of Martin Gardner's books, either "aha!" or "aha! Gotcha"
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