heres a new constant found this morning

>>> (1.39094974939078**(pi-0.5))-1.39094974939078
==
0.9999999999999867

the following..
>>> 1.39094974939078**2
1.934741205330274 +/- 1

and

((1.39094974939078**(pi-0)))
2.8198510518716056 +0/+1/+1

show up in things as varied as the density of galaxies, gasoline chemistry, traffic accident formulas, and more.

Kinda cool.

Did you solve this numerically?
x**(pi-0.5) = (1+x)

The second one sounds like it’s close to e.

this sounds like a floating point error...

@-red not sure if you mean if it was solved according to rules/solutions. If so, no. Dont have any of the analytic and equation solving background (even rudimentary) to do that. So any time anyone posts what seems like an obvious takeaway about something I missed, I'm always grateful.

Any case, just experimented with constants, and adjusted the number by hand on both sides of the equation till the output matched the input.

Had a few false starts with other attempts at finding constants in earlier posts. Bruce's constant for example, turned out to be an aproximation of another, though that was half tongue in cheek because I didnt want to look like a fool if it turned out later on that I missed something..and of course I did.

And of course there was that truncation of omega that yields the silver ratio, but fuck if I can find the post with the formula now.

@violet-isle was also surprised to discover it wasnt. I could always double check. Maybe do it eith the decimal module in python, and set the precision higher. If I do that though I'll write an automatic checker this time instead of adjusting the numbers by hand.

Reminds me of this xkcd: https://xkcd.com/217/

Another fun one found this morning:

slight modification of x from 1.3909497493907668, to

1.3919255815692

gives us

((1/log(x, pi-0.5)-1)/x)/x ==

1.00000000000239

The '..239' at the end is just a rounding error because I only approximated the constant.

and then theres this fun little aproximation of e:

where x=1.3919255815692

(1/(((((1/log(x, pi-0.5))-1))-1)*(x-1)))-(1/((((1/596.25)*17)+17)**2)) ==

2.7182818285290504

correct to ten digits.

@Lensflare btw if you hadn't made this comment I wouldn't have even tried to make the connection. How did you even catch that?

@Wisecrack now it looks like lisp

@Wisecrack I don‘t know honestly. It just popped out ^^
Maybe because you mentioned that it shows up in many other ares in the real world.

@Lensflare i'm fucking terrible with parenthesis.

Thing I always do when doing stuff like this is searching google "constant 'some number" and seeing what research papers pop up.

Like for example that number 596.25?

That shows up here F(x) = 2x3-4x2-x-15, as

P=15, Q=2, and F(P/Q) = 596.25

Probably of course a coincidence, because its a truncation of 1/((((1/((1/(((((1/log(x, pi-0.5))-1))-1)*(x-1)))-e))**0.5)/17)-1) ==

596.2536144371762

But it makes me wonder if we can't use some polynomial to find e or an approximation of it anyway.

Don't know how to do polynomials (I'm pulling from the internet) so this line of questions, while fun, is a dead end for me. It's more the domain of someone like you or pretty much anyone with a math background.

@Wisecrack I don‘t have a math background. I just love to watch youtube videos about math and some things tend to stick.

Btw, e can be represented as an infinite continued fraction. But I think it doesn’t count as a polynomial.

@Wisecrack you can approximate anything with a polynomial, that's what Taylor and Maclaurin series are. Also Fourier Series but that's for periodic functions, so it is better for like signal processing. But yeah, e also has a much simpler approximation formula than a lot of others, which is just the sum of 1/(n!) from n=0 up to whatever accuracy you want. Its a pretty basic example in any calc 2 class.

@Lensflare Riffing on what you wrote, and turned out a quick and dirty function that converges on e "quickly" (don't know how quickly relative to other methods, but eh):

https://pastebin.com/6uJVZUxE

The estimate of the f parameter actually isn't essential, the whole thing is relatively insensitive to the value of it. I think it still converges either way.

@violet-isle never took calc 2, but thats pretty cool. gotta test it now.

@Wisecrack you should 100% just like scroll through some khan academy videos to learn it in your free time, its super worth it, especially if you DONT take it through a horrible professor

@violet-isle been thinking about doing just that. Had almost forgotten about KA in particular though until you mentioned it, thanks.

Rewrote the script so the estimate of f isn't even needed, and the entire thing can be run recursively to estimate both e and f.

https://pastebin.com/vQzGMqTq

@violet-isle been thinking about doing just that. Had almost forgotten about KA in particular though until you mentioned it, thanks.

Rewrote the script so the estimate of f isn't even needed, and the entire thing can be run recursively to estimate both e and f.

https://pastebin.com/vQzGMqTq

modified the script again, to add support for decimal

https://pastebin.com/9kuLCA2w

Also noticed it wasn't converging until I realized python's math module only defines so many digits of e, lol!

So I set accuracy really high in the decimal module, imported a more accurate estimate of e, and sure enough it does in fact converge.

It's a beautiful thing to see.

Pulled the additional digits of e needed for testing from

https://math.utah.edu/~pa/math/...

You might have some fun looking at musl's math functions to see how exponentials/trig/etc are implemented.

https://git.musl-libc.org/cgit/...

Full Disclosure:
I'm totally a math nerd. I essentially run, 24/7 on live algorithms, often in place of typical human perceptions/emotional reactions, like being upset/angry(or pretending to be, in my case) when some kids keep stealing your pencils (2nd-grade-me made an excel doc with 5 X's and an iteration counter to increase the level of retaliation)

That said, I know the math, through calc 3, just rarely the proper notation and a good deal of related vocab.

If you want to find some fascinating constants... have you done much with common, naturally occuring figures? Like fibonacci, sequence or the derived spiral calculations of it? There's also some amusing patterns if you use religious numerology(666 vs 7, heptagrams 7/2 and 7/3, etc). There's a ton in biology too, especially if you get into genetics.

The project I/my company is focusing on is undoubtedly going to find some interesting numbers connected to humans. I wish I could say more without wasting the effort tons of NDAs.

@awesomeest accidentally rediscovered generating the fib sequence using phi. That happens sometimes when you cover every possible expression combination for generating a sequence.

Anycase, whatever you're working on sounds cool.

Hopefully you can talk about it more in the future.

@james2k oh I know what you're trying to say, if thats what you're getting at..

All them logarithms, inherently using e!

I'm a dirty filthy cheater.

I guess I coulda implemented a taylor series approximation, if I wanted to spend an afternoon or two learning calculus or whatever.

But the principle in the script is sound.

@james2k wait, a minute, maybe I misread you. I'm looking at log.c, and they're using

"Top 16 bits of a double. "

...dafuq?

I'm not real strong on the c code, and less on the binary math (unless I do it by hand), but whats going on here?

that looks like a lot of quake-engine bitwise magic fuckery going on to get their algorithms JUST SO.

Give me a run down on what I'm missing? What if I say please?

@Wisecrack well, by nature, I'll only be able to publicly talk about it when it's got public documentation. Basically, we are gonna quantify everything, the specifics of 'how' is the proprietary and confidential part... even moreso because an inherent byproduct of it is a new, theoretically at least, better form of data collection and extrapolation.

@awesomeest Are you the first one ever to run on live algorithms? You’re probably going to solve billions of problems per second. It’s on us to filter all that and find the solution to the problem we’re interested in at present. The other solutions will probably not make sense to us, not for centuries at least maybe.

@-red no clue if I'd be the first. we cant even prove if humans in general run on logic-based algorithms w/a monkey wrench called emotions thrown in. If we could, there's no current, or foreseeable way to know if it happened before or even if there's thousands of people, right now, doing the same thing.

That said, I'm a statistical outlier, far beyond a plausible conclusion that isnt rooted in some multifaceted, to be identified, syndrome
-Health: weird auto-immune and beyond, 3/5 most painful conditions known... typically not connected. Chronic migraines, kidney stones and rsd/crps... I'm even an outlier in each of those conditions.
-Neuro: the 2 aforementioned plus adhd and a female with autism(~4x are male).also my IQ

Basically, I'd question anyone who didn't initially assume I'm just a weird, delusional, narcissistic hypochondriac-- bordering full insanity if you inquire about my sleep behaviour or pattern recognition.

Unfortunately, I'm not. It'd be way simpler if I was.

(x^(pi-0.5))-x=1

x ≈ 1.39094974939078385610620289526146899208274078199674...

https://wolframalpha.com/input/...

@j0n4s very cool! Thank you jonas. I'd completely forgot about wolfram. Getting coffee, waking up and gonna go play with the numbers right now. :P

If you find anything else useful or interesting, I'm looking forward to reading it.

@Wisecrack sorry about the wait

I have no clue about the logs/exponentials, it looks like quake engine IEEE 754 abuse.

The trig functions do use taylor series, though.