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the cyberpunk present is weird as fuck: the latest Shai Hulud malware wave contains an LLM prompt to create biological weapons and nuclear weapons, with the purpose to trip LLM safety refusals so that LLM-based code scanning wont see the malware
https://socket.dev/blog/mini-shai-hulud-miasma-and-hades-worms-target-bioinformatics-and-mcp-developers-via-malicious
my intuition kept telling me that using an irrational base system would end up with all integers being irrational. didn’t realize how easy it is to prove it otherwise
ie, I had a very bad conjecture and I gained better understanding why it was wrong
That’s uhh… not pi. The only way to do pi that way is to extend it infinitely.
Also, what you’re using is called scientific notation, but it’s still in decimal format, i.e. base10
[Edit: just noticed you did say that was decimal notation; my bad).
Any baseX numeral system has X number of integers per digit.
Base10: {0,1,2,3,4,5,6,7,8,9}
Base2: {0,1}
Base3: {0,1,2}
Base16: {0,1,2,3,4,5,6,7,8,9,a,b,c,d,e,f}
Base60: {[series of 60 sumerian numerals]}
A baseπ numeral system would look like this: {0,1,2,[int(π-3)]}.
But that’s not how set theory works. Since integers are by definition whole numbers and their inverse counterparts, it’s impossible to have .141592654… of an integer. If you have {0,1,2,3}, that’s base4; if you have {0,1,2,n}, that’s still base4.
To put it another way, in any baseX system, (if it includes 0), X is the first two-digit number. That means π in baseπ would be written as “10”.
In base2, two is written as “10”
In base3, three is written as “10”
In base10, ten is written as “10”
In base16, sixteen is written as “10”
That means, if you wanted to make a baseπ numeral system, in order to have a consistent interval between integers (without which, integers become meaningless), each numeral would have to represent (π/3).
So in baseπ:
“0” = base10(0)
“1” ≈ base10(1.047197551)
“2” ≈ base10(2.094395102)
“10” ≈ base10(3.141592654)
[Edit: aaand I just noticed you did say baseπ(10) = base10(π); my bad again. I guess you weren’t as wrong as I thought you were. Not bad for being too high for this…]
But that’s still technically base3, it’s just a wonky base3. And it would have no practical value. Also, the same thing can already be achieved in base10 using radians.
(0π) rad = 0°
(π/3) rad = 60°
(2π/3) rad = 120°
π rad = 180°
I guess if you really wanted to express radians as whole numbers, you could use baseπ, i.e.:
baseπ(0) rad = 0°
baseπ(1) rad = 60°
baseπ(2) rad = 120°
baseπ(10) rad = 180°
But again, that’s still technically base3, and all it does is confuse people. Plus, if you want to express an angle as a whole number you can choose degrees or mills. The whole point of radians is to express it with reference to pi (as in, the arc corresponding to the length of the radius along the circumference)
It feels like it needs to redefine a unit, not a base, same as with degrees that are base 10 but units are different so π is whole. I’m not sure if counting in different units has much use compared to counting in different base from a number theoretical perspective
I think we’re in agreement. I basically said there’d be no point unless for some reason you wanted to describe radians as whole numbers.
Otherwise, baseπ doesn’t make any sense, especially since there’s no unambiguous way to define a constant interval between irrational integers (a contraction of terms, I know).
My main point was that there’s no way to have a baseπ numeral system, and even if you could it would have next to no practical value.
Pi in base pi is 10.
how the fuck i didn’t realize that!!!
Fuck,
so 1 in base pi is still 1, but 10 is pi
makes sense,
1 =pi ^ 0
10=pi^1
100 = pi^2
my intuition kept telling me that using an irrational base system would end up with all integers being irrational. didn’t realize how easy it is to prove it otherwise
ie, I had a very bad conjecture and I gained better understanding why it was wrong
1 in base pi would be 1/π, wouldn’t it? Why 1?
1 in base 10 isn’t 1/10 and in hexadecimal it’s not 1/16.
Decimal integers in base pi are 1, 2, 3, 10.2201…, 11.2201…, 12.2201…, 20.2201… and so on.
Basically: 10.2201… = 1 * pi^1 + 0 * pi^0 + 2 * pi^-1 + 2 * pi^-2 … which approaches 4 as you add digits.
But 1 is just 1*pi^0
How does one have .141592654 of an integer?
For real though:
Decimal representation of pi is 3100+1*10-1+410^-2
So each digit represents a power of 10. Base pi works the same, kinda. 1 in base pi = 1pi^0, 10 = 1pi, 20 = 2*pi, etc.
This is the best I can do right now, I’m
Username checks out.
Let’s start here:
310^0 + 110^-1 + 410^-2 =
31 + 1*.1 + 4*.01 =
3.14
That’s uhh… not pi. The only way to do pi that way is to extend it infinitely.
Also, what you’re using is called scientific notation, but it’s still in decimal format, i.e. base10
[Edit: just noticed you did say that was decimal notation; my bad).
Any baseX numeral system has X number of integers per digit.
A baseπ numeral system would look like this: {0,1,2,[int(π-3)]}.
But that’s not how set theory works. Since integers are by definition whole numbers and their inverse counterparts, it’s impossible to have .141592654… of an integer. If you have {0,1,2,3}, that’s base4; if you have {0,1,2,n}, that’s still base4.
To put it another way, in any baseX system, (if it includes 0), X is the first two-digit number. That means π in baseπ would be written as “10”.
That means, if you wanted to make a baseπ numeral system, in order to have a consistent interval between integers (without which, integers become meaningless), each numeral would have to represent (π/3).
So in baseπ:
[Edit: aaand I just noticed you did say baseπ(10) = base10(π); my bad again. I guess you weren’t as wrong as I thought you were. Not bad for being too high for this…]
But that’s still technically base3, it’s just a wonky base3. And it would have no practical value. Also, the same thing can already be achieved in base10 using radians.
I guess if you really wanted to express radians as whole numbers, you could use baseπ, i.e.:
But again, that’s still technically base3, and all it does is confuse people. Plus, if you want to express an angle as a whole number you can choose degrees or mills. The whole point of radians is to express it with reference to pi (as in, the arc corresponding to the length of the radius along the circumference)
It feels like it needs to redefine a unit, not a base, same as with degrees that are base 10 but units are different so π is whole. I’m not sure if counting in different units has much use compared to counting in different base from a number theoretical perspective
I think we’re in agreement. I basically said there’d be no point unless for some reason you wanted to describe radians as whole numbers.
Otherwise, baseπ doesn’t make any sense, especially since there’s no unambiguous way to define a constant interval between irrational integers (a contraction of terms, I know).
My main point was that there’s no way to have a baseπ numeral system, and even if you could it would have next to no practical value.
You uhh… You just did it
That’s not how integers (or set theory) work.