When did computer science theory get so hard?

http://blog.computationalcomplexity.org/2021/11/when-did-computer-science-theory-get-so.html

by furcyd • 5 years ago

225 180 5 years ago

blog.computationalcomplexity.org

Considering the founders intellectual merits, I’m going to go out on a limb and say that CS theory has been hard since day 0.

arethuza• 5 years ago

Out of interest, who do you regard as the founders of CS theory - I'd probably go for Church and Turing, but I can see arguments for others as well.

tgv• 5 years ago

Might want to add Post, Chomsky and Kleene, too.

loraxclient• 5 years ago

Tangential but may be of interest: a cool book (compilation?) that somewhat addresses this topic is ‘Ideas That Created the Future’ edited by Harry R. Lewis [0].

[0] https://mitpress.mit.edu/books/ideas-created-future

varjag• 5 years ago

Shannon, von Neumann

criddell• 5 years ago

Off topic, but Charles Petzold wrote a really great book that walks you through Turing's historic paper on computability and the Turing Machine. The book is called The Annotated Turing.

I've just started reading it and Petzold claims all you need is a decent grasp of high school mathematics.

DeathArrow• 5 years ago

Gottfried Leibnitz, David Hilbert, Kurt Gödel.

voldacar• 5 years ago

Leibniz technically

wongarsu• 5 years ago

What does "founder" mean to you? Leibniz did a lot of important foundational work 300 years ago, but at the same time CS as a separate field didn't emerge until the 1940s with pioneers like Turing.

tialaramex• 5 years ago

The nice thing about an open frontier is that it's really easy to be an innovator. If you put more than a passing thought into almost anything in the vast Terra Incognita you're faced with, you are now the world expert.

Today Grace Hopper's "compiler" wouldn't merit the name, it's just a linker loader, what's the big deal? Well the big deal was nobody had actually programmed the computer to help them program the computer before. A huge sub-discipline of computer science simply didn't exist.

Consider another discipline, metrology. Pioneers in metrology weren't doing advanced physics like you would see in a metrology lab today, they just had the insight that it sure is easier if everybody agrees how much corn this is, so they used prototypes, which is pretty much the simplest strategy but it's already a huge improvement on nothing at all. It took until this century for the last prototype (the Kilogram) to be replaced. On the route there those prototypes got a lot more sophisticated, and we learned a lot more about what it actually means to have a certain amount of a thing, so metrology got much harder.

tech_tuna• 5 years ago

Since day -1

Jensson4• 5 years ago

Computer science is an extremely young field. The parts of the field that number theorists could dabble in quickly got fleshed out and got hard as they could apply the millennia of accumulated number theorist knowledge, the parts more related to how to work with computers (such as algorithms or program structure) is still young today.

Edit: Note that the frontier of the field will always be extremely hard no matter what time you live in. The reason is that things will be poorly understood and written, there will be no good textbooks or explanations, you have to trudge through all that often without anyone to help you understand things or correct you. It took centuries for calculus to become as easy as it is today.

nemo44x• 5 years ago

Right - novel thought is always difficult. It’s looks easy and obvious looking back but that’s because, as you’ve pointed out, effective teaching exists for it that draws obvious connections.

Frost1x2• 5 years ago

It's interesting how in education and academics this is well known and understood, however the second you transition out of education/academia to the real world in industry, it's as if all this is lost/unknown or the burden is simply ignored to create a pressure on everyone doing the work. Businesses and business leaders often think novel work should be simple because that's what you trained for. You studied computer science, maybe even have your Ph.D. and therefor should be able to anything and everything possible using computers quickly and efficiently.

There's a large trench between what people expect and what reality is here.

amusedcyclist• 5 years ago

The author is actually talking about the opposite situation, where CS theory departments now have a lot more number theorists (and other mathematicians) dabbling in CS theory, which has lead to use of far more complex tools than before. (Fourier analysis of Boolean functions is one example I'm familiar with)

Jensson4• 5 years ago

It might use more connections to number theory today, but the connection was always there and to understand it you had to understand number theory to a deep level from the start. The other parts of computer science had to slowly build depth as it was new ground.

eru• 5 years ago

The frontier isn't always hard. When someone discovers a new powerful technique, there's often a wave of people just applying it to everything, and seeing what sticks.

See https://slatestarcodex.com/2016/11/17/the-alzheimer-photo/

wittycardio3• 5 years ago

The frontier was breached when someone found that powerful technique. Then it was no longer the frontier

bsedlm2• 5 years ago

It took centuries for calculus to become as easy as it is today.

it's easy to use, but it's (IMO) even harder to understand correctly than before. I'm referring to a mathematical-level understanding; i.e. you could re-invent it because of how well you undesrtand all of it.

P_I_Staker• 5 years ago

How so?

fantod• 5 years ago

If you're referring to the underlying rigorous analysis / set theory / foundations of math, it's arguably still easier to understand now that those things have been developed. Before these theories existed, your only way of truly "understanding" calculus to a similar level of detail would have been to actually develop the foundations of math, which would be impossibly hard for most people.

sircastor• 5 years ago

Once, during one of my classes I was reading an assigned paper and realized “hey, I know this guy…” it was an exciting little moment. I shared it with a friend who noted that unlike most fields, CS is young enough that many of the pioneers in it are still around.

ddlutz• 5 years ago

This has happened a few times, I've ended up reading research papers of people I work(ed) with professionally.

kevmo314• 5 years ago

I tend to think this is an outlier- for the most part, CS theory back in the 1970's did not hard math.

CS theory always had hard math. Software engineering didn't (and still mostly doesn't) but also in the 1970's software didn't exist so you could literally do anything and it would become the standard if it was pushed hard enough.

It's not like there's an intrinsic reason TCP packets are the way they are now, it's largely an arbitrary choice that we standardized on.

bo1024• 5 years ago

The author may have a different definition of "hard math" than you...

fragmede• 5 years ago

I think it's a reference to the kind of math involved, like hard science vs soft science. Not that I'm sure what soft math would be. Probabilities?

aduitsis• 5 years ago

But let us please note that the choice of α (low pass filter gain constant) in the original round trip estimator of the TCP congestion avoidance algorithm by Van Jacobson is not arbitrary.

titzer3• 5 years ago

It's not like there's an intrinsic reason TCP packets are the way they are now, it's largely an arbitrary choice that we standardized on.

IP and TCP were very carefully designed and were not much like the networking standards of the time. It wasn't an arbitrary choice any more than designing a rocket engine is an "arbitrary choice".

dahart3• 5 years ago

Parent wasn’t taking away from the intention of design; they were talking about what designs got canonized by accident. This happens everywhere: very good and very intentional designs become the de facto standard for arbitrary reasons, often just being first. Electrons being negative, Leibniz notation, musical notation and the four piece band, binary digital circuits, hamburgers, the car, and even the structure of TCP packets, are all things that got overwhelmingly popular despite the presence of good and intentional alternatives, they are largely arbitrary choices for standardization.

bbulkow2• 5 years ago

I fought in the networking wars. Implemented a lot of protocols and a lot of protocol gateways. Calling the reason for TCP winning 'arbitrary' or even softening that to 'not based entirely on technical merit' does not do justice to the entire land war in Asia that happened between about '85 and '95. If anyone cares about that period, they can do some research, otherwise, I would propose not uttering unfounded opinions.

kazinator2• 5 years ago

IP and TCP were very carefully designed

How did it happen that the byte order of the multi-byte numeric fields in TCP/IP headers is big endian, which is opposite of what most machines use now? Back then, did it look as if big endian would become prevalent?

Today, almost every host attached to an IP network has to byte swap.

The IPv6 people definitely ought to have designed a little more carefully.

Fellshard• 5 years ago

I believe what's being stated is that TCP isn't some mathematical inevitability, falling out of some discovered law, but rather a tool that was adopted because it had utility, and was certainly based on more formal findings or hypotheses.

convolvatron• 5 years ago

IP is somewhat arbitrary. TCP on the other hand really gets down the fundamentals of what's going on. its kind of like a 'from the book' protocol.

I've designed several transport protocols (don't ask) - and they are really just minor riffs on TCP.

if aliens had a fault-prone wire they wanted to send a message across over some distance - it seems quite likely they would end up with TCP

jessriedel• 5 years ago

The author explains pretty clearly what he means by "hard math" and cites many specific developments that introduced sophisticated techniques into academic CS where they weren't used before.

throwvirtever• 5 years ago

[I]n the 1970's software didn't exist

There actually was software in the 1970s, and earlier.

NikolaNovak2• 5 years ago

I found math depends on location as well. I moved around in the 90's during my University years; what was billed as exactly the same 3rd year networking course:

* University of Toronto, ON, Canada: HEAVY math; queuing theory; no computer lab, no mention on any specific stack or technology

* University of Athabasca, AB, Canada: No math; discussion on OSI Layers, TCIP/IP, SMTP, Ethernet; gateways routers switches, virtualization; lots of fun computer labs. Not technology specific - it wasn't doing Cisco certs or anything. But good working understanding of what's happening in networking world.

I always felt one university taught working software engineers; other university taught the dozen people worldwide who need to create next IPv8 :D

naasking• 5 years ago

That's weird, because I was at U of T engineering in the late 90s, took networking and they covered some math for various calculations on ring and wireless networks, had labs, and covered everything the Athabasca course covered as well. Was that for computer science or engineering?

JohnHaugeland2• 5 years ago

It's not like there's an intrinsic reason TCP packets are the way they are now

What are you talking about? It was a three year argument based extremely heavily on prior knowledge

Why does everyone think that just because they don't know what craft went into something, there wasn't any?

Ar-Curunir4• 5 years ago

No. NP-Completeness was first defined in the 70s. That’s literally a foundation of much subsequent work. The depth of techniques used back then was mostly just elementary combinatorics, probability, and number theory. In comparison, much work nowadays require complex algebra, advanced combinatorics, and deeper mathematics like measure theory.

(This is not to downplay the work of the pioneers who discovered these foundational concepts; just to point out that they used less sophisticated mathematical tools)

AnimalMuppet3• 5 years ago

What in computer science requires measure theory?

SavantIdiot• 5 years ago

Feynman used a differential equation to prove the correct size of the buffers on the first connection machine [1].

[1] https://en.wikipedia.org/wiki/Connection_Machine#Designs

rabite2• 5 years ago

It's not like there's an intrinsic reason TCP packets are the way they are now, it's largely an arbitrary choice that we standardized on.

This is incredibly off-base. There was a huge effort to force an OSI-designed networking protocol stack that was designed by a committee of government bureaucrats and big blue sales engineers. It was a total disaster, but the vast amount of resources that were dedicated to forcing the OSI memes was in the billions of dollars. Large amounts of actual physical hardware were produced conforming to protocol standards nobody doing anything real actually wanted to use because a lot of government agencies required all network equipment to be compatible with the OSI protocol stack.

TCP, UDP, and the modern routing protocols (BGP, OSPF, etc) and their associated address resolution systems were not an arbitrary choice -- they represented orders of magnitude level improvements over the government-backed OSI standards and getting them to succeed was the product of intense collective effort of some of the most brilliant minds of the past century.

https://en.wikipedia.org/wiki/Protocol_Wars

walshemj• 5 years ago

As a former OSI person (UK third line X.400/500 support ) I think that TCP/IP won as it was simpler and good enough.

TCP/IP was in no way an technical improvement over OSI

drewg123• 5 years ago

As far as I'm concerned, it was always hard. I took 2 theory classes (undergrad and grad) in the early 90s. I dreaded the proofs, and I hated the classes, and could barely stay awake for them. I'd much rather stay up all night coding a project for another class than do one proof for a theory class. Ugh.

grumple• 5 years ago

The background color on that site makes it very painful to read. Author, if you're on HN, please make this something more normal.

jodrellblank• 5 years ago

"Please don't complain about website formatting, back-button breakage, and similar annoyances. They're too common to be interesting. Exception: when the author is present. Then friendly feedback might be helpful." - https://news.ycombinator.com/newsguidelines.html

pcthrowaway• 5 years ago

Alright, but discussing how a UI is hostile to a user trying to understand the content surely falls within the HN guidelines. Chrome doesn't have a reader mode does it? I want to read the article, but it causes actual eye pain.

This isn't an annoyance like back-button breakage. It's a design issue with a very easy fix that makes it impossible to read this for (at least) some people

nickkell• 5 years ago

Normally I'd agree with you, but that website is a particularly horrendous shade of green. I had to put on sunglasses to read the article

analog31• 5 years ago

I don't know if this is an analogy, but the first thing that came to mind was: When did jazz improvisation get so hard? The answer is the Bebop era. And it could just come down to, players got sick of playing the easy stuff, so they started making up hard stuff.

evancoop• 5 years ago

I might argue that computer science theory is not fundamentally harder, so much as the available tooling is far more sophisticated. Not so many years ago, the function for mean and median needed to be written rather than accessed within native libraries.

Now, complex neural network architectures are available to all. Alas, simply gaining that access does not in any imply deeper understanding of what is occurring under the hood. Perhaps the higher technical demands is simply a byproduct of the more complex "off-the-shelf" solutions and the need to do more than simply pip install, point, and click?

mjburgess2• 5 years ago

I'd say its more the opposite. The lack of much "academic & public understanding" of neural networks comes down to the severe lack of statistical modelling and empirical theory-building knowledge in the compu-sci community.

NNs are not a hard thing to understand, it's just regression -- there's parameteric and non-parametric. And NNs are, just like any generic approximator algorithm, a largely non-parametric method. The lack of understanding of even what a parametric method is, in CS, is very telling: NB. it has nothing to do with the final model having parameters. It is whether the method assumes a parametrised distribution of its input data. Non-parameteric methods are well-understood, they aren't magic, and they aren't very hard to characterise.

Rather, it is exactly in those areas where compu-sci people are most qualified that the mathematics gets the hardest. Much of the low-hanging fruit has been picked (Turing, et al.) and today comes the hard part of the thorniest problems.

CrazyStat• 5 years ago

The lack of understanding of even what a parametric method is, in CS, is very telling: NB. it has nothing to do with the final model having parameters. It is whether the method assumes a parametrised distribution of its input data.

Having done my PhD work on (Bayesian) nonparametric methods I'm struggling to parse this.

What is the input data? Just the explanatory (independent) variables? Both explanatory and response (dependent) variables? Are we talking about a joint or conditional parametric distribution?

Many parametric methods (e.g. OLS regression) make no assumption about the distribution of the explanatory variables. Many "nonparametric" methods do make parametric assumptions about the conditional distribution of the response variable(s) conditioned on the explanatory variable(s) (e.g. GP regression).

I don't see how this works as a classification for whether a method is "nonparametric" or not.

srvmshr• 5 years ago

Computational theory was always hard. What is different now is that we see a lot of confluence to practical applications, and people who haven't exclusively trained for it find it hard to parse. It was previously in the realm of math - now there is some drift towards modern software engineering.

throwaway2016a• 5 years ago

Anecdotally:

I went to a college in Boston in early 2000s for my CS degree and it was undergoing extra ABET accreditation to put it in line with the engineering programs. The prior year has mostly algebra based course work but due to the change: all our math (including physics) was switch to calculus based just like the other engineering programs. And the theory courses got more in depth.

So if I had to guess based on my personal experience I'd say added rigor is possibly due to the field becoming less like a free-for-all and more like engineering.

In other words, knowing why something works vs just experimenting until you stumble upon something that works.

I've always appreciated a B.Sc. or M.Sc. in Computer Science as the academically rigorous cousins of Associate degrees, B.A., and bootcamps. You can get a job with both types of education but one understands the theory behind things far better.

Edit: Not sure if it is like this globally so just as an FYI... B.Sc. and M.Sc. are Bachelor and Master of "science" degrees where as B.A. is in the Liberal Arts. In the US you have CS degrees in both. The B.A. is more well rounded but the B.Sc. is more rigorous in theory and math.

sumtechguy• 5 years ago

What degree you get kind of depends on which college you went to and when. The difference in my school between the eng track and the arts track was basically 2 classes between the two programs. Both programs were run by the same professors. If I had got the degree 10 years earlier I would not have been able to get it and only could have gone math with a study in CS. As is, I think my CS program was 6 hours away from an additional math degree. Which makes sense as the math programs typically were supersets of the CS degree for a long time. I do not know about the time after but from what I heard they simplified the program a bit and went more algerbra/java like you said.

lanstin3• 5 years ago

The original article is not about these things. It is about the difficulty of the rigor increasing. From some sort of easy encoding of computation into integer math to doing Fourier analysis over booleans. From maths you can grok in a few hours to the horrendously complex stuff in number theory that takes days and you aren’t really sure you get it.

In neither case is it a matter of theory vs practice. It is that the mechanics used by theorists is a lot more difficult than a few decades ago.

Actual software development becoming like engineering, which seems counter to my experience, is a different issue.

In my experience software veers away from engineering because as soon as something is standardized enough to not be novel, it’s completely captured by a library or service or something and is a solved problem. The new software is always doing something new. And there are no lessons learned, except, ironically, at the deep theory level.

fortran77• 5 years ago

It was really easy when I got my graduate degree in 1984. Don't know if I'd be able to do it today. (And yes, I'm serious).

My undergraduate degree was in math, and I switch to CS for graduate work because math got too hard.

dekhn4• 5 years ago

I took only one CS class in college- taught by David Huffman. It was a wonderful class, most of it beyond me (I was a bio major who liked hacking) and I ultimately failed. So, IMHO it was definitely hard math (sphere packing, prefix-free codes) back in the 90s and I'm sure before that.

Amusingly, that failure so drove me to learn computer science that I'm now an expert, but I often get stuff like order calculations wrong because they don't correspond well with actual computer performance.

nostrebored• 5 years ago

Talking about theory as a single subdomain of CS doesn’t really make sense anymore. It’s a wide and varied field. I have friends who work mainly in automata and complexity and have worked with people focused exclusively on a single class of algorithms.

They’re remarkably different in difficulty.

My friend in complexity is clearly a mathematician. My friend who is an expert in random algorithms is doing a lot more throwing darts at a dartboard with enough theory chops to make his papers interesting.

I studied CS theory and modeling in university and my degree was effectively a math degree. Without the math and analysis piece I don’t think the theory ever would’ve been intuitive.

kaymanb• 5 years ago

I think it's interesting that we seem to equate CS Theory being hard with involving sophisticated math. Are there any examples of concepts in Theory that are considered hard, but not because of their dependence on math?

The article seems to focus on complexity theory, but I couldn't think of any from that sub-field. My first thought is the Paxos algorithm for distributed consensus [1], which definitely has a reputation of being difficult to understand, and fits under the Theory umbrella.

[1] https://en.m.wikipedia.org/wiki/Paxos_(computer_science)

lanstin3• 5 years ago

Yeah I think a model of computation set in Minkowski space time is novel compared to classic theory of computation, which is sort of set in Plato land.

titanomachy• 5 years ago

I wonder if Paxos is actually considered hard to understand by academic computer scientists, or if it just happens to be harder than most of the algorithms that practicing software engineers regularly try to understand.

Disclaimer: I'm a software engineer who doesn't understand Paxos.

mindcrime3• 5 years ago

I'm not sure what the answer to this question is in general, but from my perspective (was a CS major in the mid 1990's) there were definitely parts of this that were hard (by my standards) by then. All of the computational complexity stuff (P vs NP, etc.) feels akin to black magic to me. Especially so when you get into that whole "complexity zoo" thing where there are 10 bazillion different complexity classes. To this day I have no idea what most of them mean and have to visit the corresponding Wikipedia page and read up on any ones that I encounter.

wespiser_2018• 5 years ago

I'd say it was "hard" all along. The question of computability is challenging in that it requires a good deal of formalism and theory to get anywhere near problems we deal with every day.

Take NP-Complete for instance. We know a problem is NP-Complete if we can do a Karp Reduction from another NP-Complete problem and also prove the problem is in NP. Sure, that's fine. But how was the first NP-Complete bootstrapped? Well, using automata and generalized turning machine languages! You can use NP-Complete as a concept at work, and never touch the original proof using a non-determistic turning machine language.

That's at least one course worth of material to teach in order to get students to understand automata. To me: that's a complex approach to a simple question: what can we compute? We have to invent a series of automata with increasing complexity and corresponding theories/proofs. I don't think it's bad, it's just the nature of the problem!

Ar-Curunir4• 5 years ago

The point is that one catch up to state-of-the-art-in-the-90s in CS theory with basically one upper-division course. That is not a lot from from a mathematical perspective.

Till a few years ago, undergrads could contribute to CS theory research, whereas in math only senior grad students can do that.

What the article is saying is that CS theory is slowly moving towards the latter model, as more work is done and the low-hanging fruits are picked off.

kazinator2• 5 years ago

When did security get so hard? It used to be that you could assume that the supervisor mode of your CPU was safe from the user mode. Ah, the good old days.

jeffreyrogers3• 5 years ago

On the math page that he linked he has some ideas:

1) When you get older math got harder.
2) When math got more abstract it got harder. Blame Grothendieck.
3) When math stopped being tied to the real work it got harder. Blame Hardy.
4) Math has always been hard. We NOW understand some of the older math better so it seems easy to us, but it wasn't at the time.
5) With the web and more people working in math, new results come out faster so its harder to keep up.
6) All fields of math have a period of time when they are easy, at the beginning, and then as the low-hanging fruit gets picked it gets harder and harder. So if a NEW branch was started it might initially be easy. Counterthought- even a new branch might be hard now since it can draw on so much prior math. Also, the low hanging fruit may be picked rather quickly.

Personally I think it is mostly 2 and 3. And a lot of it has to do with how math is communicated. The very abstract way that math textbooks use to communicate is not how most mathematicians think when solving problems. A lot of things I struggled to learn from books became much more understandable once someone gave me the little insight I needed to make sense of it in conversation.

ericbarrett3• 5 years ago

I completely agree regarding books. I've been refreshing my university undergrad-level math, and older textbooks have been much more accessible than most written after (roughly) the 1990s, even though the subjects haven't changed at all—this isn't avant-garde stuff. Seems no field is exempt from the modern "churn for churn's sake" phenomenon.

bigthymer• 5 years ago

older textbooks have been much more accessible than most written after (roughly) the 1990s

Why? How are they different?

hungryforcodes2• 5 years ago

In Grade 12, I had a revelation when a good friend explained to me in 5 minutes that trigonometry was largely just ratios. I guess either it hadn't been explained to me before properly or I didn't understand it at a DEEP level, but when he laid it all out for me on the board, it was suddenly all so simple.

I had three reactions:

1) I was elated to finally understand sin and cosin.

2) I was thankful for him and also amazed at how simple it was in 5 minutes to explain something that seemed to have eluded me for 5 years of highschool. It made me wonder alot what other difficult subjects could be easily taught by just a good explanation.

3) I wondered why math class had failed so specifically to give me that knowledge, or at least test me to see if I understood it and if I didn't to ensure that I did understand it. The answer I think was math class just encouraged me to use a calculator, thus short circuiting any real understanding.

Anyways he went on to be a physics professor at Cambridge.

I always appreciated that moment.

blocked_again• 5 years ago

older textbooks have been much more accessible than most written after (roughly) the 1990s

Explain?

runnerup2• 5 years ago

As a related side note, I'm looking for a post on HN from earlier this year which linked to a textbook from the early 1900's or late 1800's about visualizing data. If anyone can help me find it, I'd greatly appreciate it.

Jensson4• 5 years ago

How much math have you studied? I think they are talking about grad level math courses where things starts to get really abstract. Calculus, linear algebra and discrete math are all super concrete, pretty sure they are talking about things described as "generalized abstract nonsense": https://en.wikipedia.org/wiki/Abstract_nonsense

Try reading the example on that page. That is what makes math hard. Not the way calculus is described.

m0lecules• 5 years ago

Or try reading the ethereum yellow paper: https://ethereum.github.io/yellowpaper/paper.pdf

When it gets into the symbolics of the ethereum state machine (section 4+), things get hairy fast. Unfortunately papers like this only make sense once you understand the paper. It's a succinct representation of knowledge for someone skilled in the field, but not a sensible way to teach others about the EVM.

jeffreyrogers3• 5 years ago

I had a math minor in college and took some upper level analysis courses, so I know what abstract means in the context of higher mathematics. I wasn't talking about calculus.

agumonkey• 5 years ago

Well they are concrete and not so much, for instance e being it's own derivative only started to make sense to me when I got the 'abtract algebraic' (fix point, neutral element, self similarity) thinking. Otherwise it was a fuzzy if not empty property.

Jenk• 5 years ago

things described as "generalized abstract nonsense": https://en.wikipedia.org/wiki/Abstract_nonsense
In mathematics, abstract nonsense, general abstract nonsense, generalized abstract nonsense, and general nonsense are terms used by mathematicians to describe abstract methods related to *category theory* and homological algebra.

Oh so _that_ is why I can't understand Haskellers..

mcguire• 5 years ago

I don't think 6 has applied to math for hundreds of years, but I do see it as having applied to CS relatively recently.

bumby• 5 years ago

A lot of things I struggled to learn from books became much more understandable once someone gave me the little insight I needed to make sense of it in conversation.

Don't just leave us hanging :-) Care to elaborate on what helped gain that insight?

hinkley• 5 years ago

Randall Munroe has a strip about how all the math most people need is how to fairly split a bill for a birthday dinner (so that the guest of honor doesn't pay).

I sometimes wonder if we'd be better off telling teenagers that the motivation they need to learn math is self-preservation. There are always people who are going to try to trick you with bad math (from misleading cost/benefit analysis, to financial malfeasance, to bad faith public policy debates) and if you know some math they can't do that to you.

The "you give Timmy five apples" shtick is almost anathema to that. You've practically built a narrative for the kid to get distracted from the point of the exercise. I don't like Timmy, or I don't know who the hell Timmy is. I'm not giving him five of my apples. Timmy can go fuck himself. Get your own damn apples.

Better: you put twenty skittles into a cup. You drop the cup, and there are only 5 skittles left in the cup. How many are on the floor/how many do you need to replace the lost ones?

emodendroket• 5 years ago

That would seem to imply that there's little point in learning algebra, let alone anything more advanced than that.

late2part• 5 years ago

Timmy's actually pretty cool. I'd recommend you give him a chance. Plus he tends to return more apples than you give him.

BLKNSLVR2• 5 years ago

Classic "lies, damn lies, and statistics".

I need to start collecting examples of conclusions drawn from incomplete and / or poorly explained statistics. I did three levels of statistics, and found it boring because I struggled to find how it would be useful in my future career. I'm eternally annoyed at myself for not paying enough attention, I love stats now.

One interesting (and divisive) example for statistics was way early in the COVID timeline the talk about reaching herd immunity through "just letting it propagate" as per the narrative around Sweden's approach.

The required herd immunity figure was something like 60%[0] at the lowest end. In the US daily new infections peaked in January 2021 at 305,000[1], and the US population is around 330 million[2] (with 60% being 198 million).

At that maximum rate of new daily infections, it would take 649 days (1.77 years) to reach herd immunity.

The average daily new infection rate from the 21st of March 2020 to the 15th of November 2021 is ~79,500. At that rate it would take 2,490 days (6.8 years) to reach herd immunity.

In both of the above scenarios, with a fatality rate of 1%, there would be 1.98 million deaths during the time span.

Other numbers that would be interesting in context:

- Number of hospital beds

- Number of ventilators, how quickly they can be manufactured, how long they're dedicated to an individual case (and bonus points for recovery rates of those who needed to use a ventilator)

- Medical oxygen usage rate and availability (India had an issue with running out of medical grade oxygen[3], although it may not be as much of an issue for more countries with more advanced infrastructure)

Thank fuck for medical technology and vaccine development (the age we live in!)

[0] https://www.sciencemediacentre.org/expert-comments-about-her...

[1] https://www.worldometers.info/coronavirus/country/us/#graph-...

[2] https://en.wikipedia.org/wiki/Demographics_of_the_United_Sta...

[3] https://www.theguardian.com/world/2021/apr/29/explainer-why-...

actually_a_dog• 5 years ago

Mention of Fourier transforms over fields other than the complex numbers brought this up to mind: https://en.wikipedia.org/wiki/Sch%C3%B6nhage%E2%80%93Strasse...

TL;DR: It's a way to multiply n-digit integers in time O(n log n * log log n) time, developed in the early 70s, using DFTs in the ring Z mod 2^k + 1, with a slightly clever choice of k. Since the runtime was so tantalizingly close to O(n log n), it fueled speculation that O(n log n) was the optimal runtime. This bound was finally proven in 2019: https://hal.archives-ouvertes.fr/hal-02070778v2

Otternonsenz2• 5 years ago

As someone whose childlike wonder piques at the technology I grew up with, I've always tried to delve into any parts of knowledge I could get my head around; I read textbooks/papers/articles until I come across something I don't get, then drill down into that until I get it.

However, because my education/training has not been part of an institution, I do feel like I am on the outside of understanding when it comes to wrangling the lightning inside the rocks we work on day in/day out. I've been both DevOps (helpdesk jockey to admin) and dabbled in frontend work, but mostly fell into those positions and grew into them.

Couldn't tell you how to work with Kubernetes or Docker, but have been following discourse on here enough to understand how they are useful for big stuff. I used PuTTY back in HS to work on a backend internship, but have no clue why it works. I have made at least 2 programs still running internally at a big real estate tech company, but cannot deploy my own apps on my own computer.

Is this disconnect with deeper Computer Science theory just my issue as a visual and kinetic learner? Is the understanding of modern technology only suitably captured in a classroom setting that I do not have access or time for?

winternett• 5 years ago

Docker is basically a way to segment/emulate control, configuration, and access to cloud host infrastructure on an individual basis because in shared hosting environments, you can't change settings or they can possibly compromise security and impact everyone else hosted on the platform negatively. It adds a bunch of software on top of other software and requires massive hardware and power consumption to drive it overall, and still is not particularly more reliable nor secure than the old method of hosting your own site, and it drives consumerism and environmental pollution probably just as bad if not worse than before here and in many other parts of the country, but it generally feels less guilty because you don't have to see the factories and plants -- they're hidden overseas and in rural areas that you don't go to.

No one wants to admit that things were probably better when we ran our own infrastructure and bought hosting at fixed pricing, because they're busy making money off of the new and overly-complex "utility priced" cloud hosting solution model to hosting web sites and apps, and because the learning curve for their competition is now more steep, reducing the threat to their profit pipelines... There, I said it.

These days people have a huge problem with getting to the point in speech and in writing. If you put the premise up front, it allows people to get it an move on, or to argue with you online more easily without reading the elaboration below it.

There is usually a reason why software and hardware is made, to solve a specific problem, or to solve a group of problems, yet modern-day engineers don't see the importance of putting the detail about the problem(s) that their tools solve foreword FIRST AND FOREMOST before gushing about how to use their tools. A lot of the time they don't put the premise first because it's an ugly solution, or in reality simply useless, or based on being costly, and usually just too damn overly-complicated to really work consistently and accurately.

We also have marketers, managers, and sales people working to promote ideas without any real understanding about the reason why those things were created. Many people simply don't care as long as their share values increase or if they make a paycheck, so there's even more of a barrier to meaningful answers to why in the he|| things exist, to determining real meaningful fixes to modern-day problems, and to why certain solutions are different than other things used to solve already over-complicated IT problems.

Life is better when it's more simple, simplifying things frees up time to innovate beyond just ideas that are geared towards making profit. The world would be a far better place if we began a shift towards bringing technology back down to earth, and if everyone would stop chasing the annual "tech leader supreme monopolistic empire douchebag" awards.

908B64B1972• 5 years ago

Docker will make sense if you had a good OS class. The summary is that it makes it easier to run and deploy software and gives extra control over resource access and isolations between programs.

Kubernetes will immediately make sense if you take a serious Distributed Systems class.

Otternonsenz2• 5 years ago

Thank you!

I have some books on both OS and Distributed Systems (gotta love goodwill finds), and appreciate the pointer towards where I can deep delve on how these work at a deeper level :)

dehrmann• 5 years ago

Well that's a background color I haven't seen since 1999. It even messes with my eyes when I click back. To reader mode, with you.

cweill• 5 years ago

Sightly OT: the best Math for Computer Science book/course I ever read is the one from MIT https://ocw.mit.edu/courses/electrical-engineering-and-compu...

Prof. Tom Leighton is an incredible teacher who teaches the intuition before the theory.

bob331• 5 years ago

Who cares. I’m earning fat bucks and I know none of this

doofin• 5 years ago

As math is becoming harder,we also have better tool to tackle such complexity.For example,it's probably easier to use a theorem prover which supports homotopy type theory to study algebraic topology and synthetic homotopy theory.However,the problem is that we have to understand homotopy type theory first.

mgaunard• 5 years ago

Computer Science got harder once you realized it existed outside of undergraduate studies.

ProfHewitt• 5 years ago

Computer science theory didn't get harder.

Instead, education became weaker :-(

See following link for foundations of computer Science:

https://www.youtube.com/watch?v=AJP1VL7shiI

chobytes• 5 years ago

Probably reflects one's interests more than anything. If you want some easy results you try to work in younger parts of the fields. Or if youre really lucky and a little clever, some of your own novel thoughts might go somewhere interesting.

When did computer science theory get so hard?

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