#Computer science

[captaindrewboy]

I hate when I tell people I'm into Comp Sci and programming and they go "ooh there's a lot of money there". I'm not DOING it for the MONEY I'm DOING it because I want to FUCK the COMPUTER!!!!

[lilith-hazel-mathematics]

Self-referencing functions

Hey mathblr, let me tell you about one of our favorite foundational systems for mathematics! It's designed to allow for unlimited self-reference, which is neat since self-reference is usually thought of as a big no-no in foundational systems. It turns out that it actually doesn't matter at all, because the power of self-reference is completely exhausted by the partial computable functions. The theory ends up being equivalent to Peano Arithmetic.

What are the axioms?

The theory is two-typed: the first type is for the natural numbers, and the second type is for functions between numbers. For convenience, numbers will be represented by lowercase variables, and uppercase variables represent functions. To prevent logical contradictions, we permit that some functions will fail to evaluate, so we include a non-number object ☒ called "null" for such cases. The axioms about numbers are basically what you'd expect, and we only need one axiom about functions.

The < relation is a strict total order between numbers.

Each nonempty class has a minimum: axiomatize the "min" operator with φ(n) ⇒ ∃m,(φ(m) ∧ min{k:φ(k)}=m≤n) for each predicate φ, and relatedly min{k:φ(k)}=☒ ⇔ ∀n, ¬φ(n).

Numbers exist: ∃n,n=n

There's no largest number: ∀n,∃k,n

There's no infinite number: ∀n,n=0 ∨ ∃k,n=S(k)

Every functional expression represents a function object that exists: ∃F, ∀(a,b,c), F(a,b,c)=Ψ for any function term Ψ. The term Ψ may mention F.

To clarify the fifth axiom, we define 0:=min{n : n=n}, and relatedly S(k):=min{n : k<n} is the successor function. The sixth axiom allows us to construct self-referencing functions using any "function term". Basically, a term is any expression which evaluates numerically. Formally, a "function term" is any well-formed formula generated from the following formation rules.

"n" is a term; any number variable.

"F(Θ,Φ,Ψ)" is a term, whenever Θ,Φ,Ψ are terms.

"Φ<Ψ" is a term, whenever Φ,Ψ are terms.

"min{n : Ψ}" is a term, whenever Ψ is a term.

In the third rule, we seem to be using the boolean relation < as if it were a numerical operator. To clarify this, we use the programmer convention that true=1 and false=0, hence (n<k)=1 whenever n<k is true, and otherwise it's zero. Similarly in the fourth rule, when we use the numerical function term Ψ as the argument to the "min" operator, we interpret Ψ as being false whenever it's 0, and true whenever it's positive. Formally, we can use the following definitions.

(n<k) = min{b : k=0 ∨ ((n<k ⇔ b=1) ∧ n≠☒≠k)} min{n : Ψ(n)} = min{n : 0<Ψ(n) ∧ ∀(k<n),Ψ(k)=0}

Okay, what can it do?

The formation rules on functions actually gives us a TON of versatility. For example, the "<" relation can be used to encode literally all boolean logic. Here's how you might do that.

¬x = (x<1) (x≤y) = ¬(y<x) x⇒y = (¬¬x ≤ ¬¬y) x∨y = (¬x ⇒ y) x∧y = ¬(¬x ∨ ¬y) (x=y) = ((x≤y)∧(y≤x)) [p?x:y] = min{z : (p∧(z=x))∨(¬p∧(z=y))}

That last one is the ternary conditional operator, which can be used to implement casewise definitions. If you wanna get really creative, you can implement bounded quantification as an operator, which can then be used to define the supremum/maximum operator!

∃[t<x, F(t)] = (min{t : t=x ∨ ¬F(t)}<x) ∀[t<x, F(t)] = ¬∃[t<x, ¬F(t)] sup{F(t) : t<x} = min{y : ∀[t<x, F(t)≤y]}

Of course, none of this is even taking advantage of the self-reference that our rules permit. For example, we could implement addition and multiplication using their recursive definitions, provided we define the predecessor operation first. Alternatively, we can use the supremum operator as a little shortcut.

x+y = [y ? sup{succ(x+t) : t<y} : x] x*y = sup{(x*t)+x : t<x} x^y = [y ? sup{(x^t)*x : t<y} : 1]

Using the axioms we established, basically as a simple induction, it can be proved that these operations are total and obey their ordinary recursive definitions. So, our theory is at least as strong as Peano Arithmetic. It's not hard to believe that our functions can represent any partial computable function, and it's only a little harder to prove it formally. Conversely, all our axioms are true when restricted to the domain of partial computable functions, so it's consistent that all our functions are computable. In particular, there's a straightforward way to interpret each function term as a computer program. Since PA can quantify over computable functions, our theory is exactly as strong as PA. In fact, it's basically just a definitorial extension of PA. Pretty neat, right?

Set theory jumpscare

Hey didn't you think it was weird how we never asserted the axiom of induction? We asserted wellfoundedness with the minimization operator, which is basically equivalent, but we also had to deny infinite numbers for induction to work. What if we didn't do that? What if we did the opposite? Axiom of finity unfriended, our domain of discourse is now the ordinal numbers. New axioms just dropped.

There's an infinite number: ∃w, 0≠w ∧ ∀k, S(k)≠w

Supremums: (∀(x≤a),∃y,φ(x,y)) ⇒ ∃b,∀(x≤a),∃(y≤b),φ(x,y)

Unlimited Cardinals: ∀a, ∃b, #(a)<#(b), where #(n) denotes the cardinality operation.

Each of the above axioms basically just assert the existence of larger and larger ordinal numbers, continuing the pattern set out by the third and fourth axioms from before. Similar to how the previous theory could represent all computable functions, this theory can represent all the ordinal recursive functions. These are the functions which are representable using an Ordinal Turing Machine (OTM). Conversely, it's consistent that all functions are ordinal recursive, since each function term can be interpreted as a program that's executable by an OTM. Moreover, just like how the previous theory was exactly as strong as PA, this theory is exactly as strong as ZFC.

It takes a lot of work to interpret ZFC, but basically, a set can be represented by its wellfounded and extensional membership graph. The membership graphs can, in turn, be encoded by our ordinal recursive functions. Using the Supremums axiom, it can be shown that the resulting universe of sets obeys a version of the Axiom of Replacement, which can be used to prove the Reflection Theorems, ultimately leading to the Specification Axiom. By adapting similar techniques relative to some regular cardinal, it can then be shown that every set admits a powerset. Lastly, since our functions are basically generated from infinitary computer code, they can be encoded by finite strings having ordinal numbers as symbols. Those finite strings are wellorderable, which induces a global choice function, proving the Axiom of Choice. Excluding a few loose ends, this covers all the ZFC axioms, giving the desired interpretation.

In the finitistic version of this theory, we made the observation that the theory was basically just a definitorial expansion of PA. In the infinitary case however, we unfortunately cannot say the same about ZFC. This ultimately comes down to the fact that our theory provides explicit and definable choice functions, meanwhile ZFC cannot. Although ZFC guarantees that choice functions exist, it cannot prove the existence of a definable choice function. This is because ZFC is an inferior theory has no clue where its sets come from, or what they really look like. Our theory, built from unlimited self-reference, and interpreted under the banner of ordinal recursive functions, is instead equivalent to the theory ZFC+"V=L".

[a-blue-mask]

I'm just a man.

[moastudiess]

04.30.2025~ Daily Productivity Challenge 6/10

Probabilities and effective study rituals before my last final exam :))

I’ve fully claimed my boyfriends’ room while he went long boarding and I’m planning on compiling every possible set of notes I can get my hands on for this open note exam

[prokopetz]

Wrong: Ada Lovelace invented computer science and immediately tried to use it to cheat at gambling because she was Lord Byron's daughter.

Right: Ada Lovelace invented computer science and immediately tried to use it to cheat at gambling because that was the closest you could get in 1850 to being a Super Mario 64 speedrunner.

[allie-leth]

"oh, nevermind, I got it working" - posted 11 years ago, end of thread.

I HATE YOU WITH EVERY FIBER OF MY BEING

[feyosha]

Computers are very simple you see we take the hearts of dead stars and we flatten them into crystal chips and then we etch tiny pathways using concentrated light into the dead star crystal chips and if we etch the pathways just so we can trick the crystals into doing our thinking for us hope this clears things up.

[commieclimbercatboy]

Girl, are you a hash function? 'cause you have an unpredictable effect on people, and I don't think I can go back to being the person I was before I met you

[microwavedmetal]

This is as unhinged as this laptop soon will be

[c-u-c-koo-4-40k]

What should you bring to school?

For the people of Gaza, the memories of days spent in school are distant. But education is not Only a Right but a Duty.

Meet Anas and Ahmad, they are related to Osama Basil, who has his own gofundme.

While managing his own gfm, Osama is also trying to help Anas and Ahmed fund their education somewhere safe, away from the Turmoil in Gaza.

They are Bright Wonderful students who want to pursue careers in computer business and medicine!

Please give some time to this Verified campaign!

Current Funding

€4,870 / €29,000

~16% Funded

Tag List for Reach DM me for Removal

And to others putting me in mentions I am So Sorry I'm not getting to many of them, I'm trying to balance between DM campaigns, ask campaigns and the mentions I get each day.

@a-shade-of-blue @sunnylittledragon

@selflovejolteon @virovac

@frustrated-froglet @qattdraws @heydreamchild

@amvs @boosting-donations

@sweet-honey-bunnies

@dyspunktional-leviathan

@nobelgasxenon

@zone0neko

@comrademango

[riseandshinemysisters]

grad school preparations

going to start preparing for my phd apps today... i know its a bit too soon considering im just a sophomore in uni, but i figured i'd go here to start giving updates about it :)

[1863-project]

Okay, I've been having trouble finding this, but I know it existed because my dad showed it to me multiple times.

My dad, recently retired, had a 40+-year IT career starting in the 1980s. (His biggest claim to fame is writing the programming for the printer driver for a program called PC Paintbrush, which was purchased by Microsoft and became Microsoft Paint, but I digress.) When I was a kid, he showed me an Easter egg snuck into an early Windows operating system where if you typed in a certain command an animation of Bill Gates as Godzilla would show up and start using his breath to zap people into Windows logos. I know it existed and isn't something I imagined because he pulled it up for me upon request multiple times, but seeing as this was the 1990s and I was a child I didn't have the details, like what OS it was. (My best guess would be 95 or 98.) I just want to see if I can recover that animation and document its existence somehow, but I haven't been able to find anyone else looking for it or who knows about it.

Any leads or information you might have would be super helpful! Thanks in advance!

UPDATE FROM DAD: it was on the desktop, you got it to show up by inputting a key sequence that he doesn't remember, and he's pretty sure it was Windows 98.

[nasa]

LaRue Burbank, mathematician and computer, is just one of the many women who were instrumental to NASA missions.

4 Little Known Women Who Made Huge Contributions to NASA

Women have always played a significant role at NASA and its predecessor NACA, although for much of the agency’s history, they received neither the praise nor recognition that their contributions deserved. To celebrate Women’s History Month – and properly highlight some of the little-known women-led accomplishments of NASA’s early history – our archivists gathered the stories of four women whose work was critical to NASA’s success and paved the way for future generations.

LaRue Burbank: One of the Women Who Helped Land a Man on the Moon

LaRue Burbank was a trailblazing mathematician at NASA. Hired in 1954 at Langley Memorial Aeronautical Laboratory (now NASA’s Langley Research Center), she, like many other young women at NACA, the predecessor to NASA, had a bachelor's degree in mathematics. But unlike most, she also had a physics degree. For the next four years, she worked as a "human computer," conducting complex data analyses for engineers using calculators, slide rules, and other instruments. After NASA's founding, she continued this vital work for Project Mercury.

In 1962, she transferred to the newly established Manned Spacecraft Center (now NASA’s Johnson Space Center) in Houston, becoming one of the few female professionals and managers there.  Her expertise in electronics engineering led her to develop critical display systems used by flight controllers in Mission Control to monitor spacecraft during missions. Her work on the Apollo missions was vital to achieving President Kennedy's goal of landing a man on the Moon.

Eilene Galloway: How NASA became… NASA

Eilene Galloway wasn't a NASA employee, but she played a huge role in its very creation. In 1957, after the Soviet Union launched Sputnik, Senator Richard Russell Jr. called on Galloway, an expert on the Atomic Energy Act, to write a report on the U.S. response to the space race. Initially, legislators aimed to essentially re-write the Atomic Energy Act to handle the U.S. space goals. However, Galloway argued that the existing military framework wouldn't suffice – a new agency was needed to oversee both military and civilian aspects of space exploration. This included not just defense, but also meteorology, communications, and international cooperation.

Her work on the National Aeronautics and Space Act ensured NASA had the power to accomplish all these goals, without limitations from the Department of Defense or restrictions on international agreements. Galloway is even to thank for the name "National Aeronautics and Space Administration", as initially NASA was to be called “National Aeronautics and Space Agency” which was deemed to not carry enough weight and status for the wide-ranging role that NASA was to fill.

Barbara Scott: The “Star Trek Nerd” Who Led Our Understanding of the Stars

A self-described "Star Trek nerd," Barbara Scott's passion for space wasn't steered toward engineering by her guidance counselor. But that didn't stop her!  Fueled by her love of math and computer science, she landed at Goddard Spaceflight Center in 1977.  One of the first women working on flight software, Barbara's coding skills became instrumental on missions like the International Ultraviolet Explorer (IUE) and the Thermal Canister Experiment on the Space Shuttle's STS-3.  For the final decade of her impressive career, Scott managed the flight software for the iconic Hubble Space Telescope, a testament to her dedication to space exploration.

Dr. Claire Parkinson: An Early Pioneer in Climate Science Whose Work is Still Saving Lives

Dr. Claire Parkinson's love of math blossomed into a passion for climate science. Inspired by the Moon landing, and the fight for civil rights, she pursued a graduate degree in climatology.  In 1978, her talents landed her at Goddard, where she continued her research on sea ice modeling. But Parkinson's impact goes beyond theory.  She began analyzing satellite data, leading to a groundbreaking discovery: a decline in Arctic sea ice coverage between 1973 and 1987. This critical finding caught the attention of Senator Al Gore, highlighting the urgency of climate change.

Parkinson's leadership extended beyond research.  As Project Scientist for the Aqua satellite, she championed making its data freely available. This real-time information has benefitted countless projects, from wildfire management to weather forecasting, even aiding in monitoring the COVID-19 pandemic. Parkinson's dedication to understanding sea ice patterns and the impact of climate change continues to be a valuable resource for our planet.

Make sure to follow us on Tumblr for your regular dose of space! 

[cheekios]

Rationing Insulin.

Blood sugar reading this morning. The average blood sugar reading should be between 60mg/dl - 100mg/dl. I am terrified of not being able to administer my insulin simply because I was too poor to afford it. I am strongly in need of community help.

CA: $HushEmu

PP: emuslayter@gmail.com

I am happy to announce I raised $33 🎉 I only need $417 to get my prescription

[prokopetz]

What I really appreciate about The Talos Principle 2 is that big chunks of its writing genuinely read like they were written by someone who's personally had to justify the discipline of philosophy to a STEM major. "There exists an implicit moral algorithm in the structure of the cosmos, but actually solving that algorithm to determine the correct course of action in any given circumstance a priori would require more computational power than exists in the universe. Thus, as we must when faced with any computationally intractable problem, we fall back on heuristic approaches; these heuristics are called 'ethics'." is a fascinating way of framing it, but then I ask why would you explain it like that, and every possible answer is hilarious.