What is theoretical computer science?
cacm.acm.org
cacm.acm.org
>Theoretical physics is highly mathematical, but it aims to explain and predict the real world. Theories that fail at this “explain/predict” task would ultimately be discarded. Analogously, I’d argue that the role of TCS is to explain/predict real-life computing.
as well as the emphasis on the difference between TCS in Europe and the US. I remember from the University of Crete that the professors all spent serious time in the labs coding and testing. Topics like Human-Computer Interaction, Operating Systems Research and lots of Hardware (VLSI etc) were core parts of the theoretical Computer Science research areas. This is why no UoC graduate could graduate without knowledge both in Algorithms and PL theory, for instance, AND circuit design (my experience is from 2002-2007).
I strongly believe that this breadth of concepts is essential to Computer Science, and the narrower emphasis of many US departments (not all) harms both the intellectual foundations and practical employment prospects of the graduate. [I will not debate this point online; I'll be happy to engage in hours long discussion in person]
Now, theoretical physics is a bit of a troubled child however in recent years.
If we map computer science aspects in not the four physics disciplines, we get:
Software / hardware engineering
Applied computer science
Theoretical computer science
Mathematics dealing with problems inspired by computer science
No this guy doesn’t get it. He doesn’t understand what science is.
In science nothing can be proven. If I say all swans are white as my hypothesis this statement can never be proven because I can never actually verify that I observed all swans. There may be some swan hidden on earth or in the universe that I haven’t seen. Since the universe is infinite in size I can never confirm ever that I’ve observed all swans.
However if I observe one black swan it means I falsified the entire hypothesis. Thus in science and in reality as we know it nothing can be proven… things can only be falsified.
Math on the other hand is different. Math is all about a made up universe where axioms are known absolutely. It has nothing to do with observation or evidence in the same way science does. Math is an imaginary game we play and in this game it is possible to prove things.
This proof is the domain of mathematics… not science. Physics is a science because it involves gathering evidence and attempting to falsify the hypothesis.
Einstein said it best: “No amount of experimentation can ever prove me right; a single experiment can prove me wrong”
Basically newtons laws of motion are a perfect example of falsification via experimentation with relativity later being confirmed as the more accurate theory that matches more with observation.
So what’s the deal with computer science?
First of all the term already hits the first nomenclature issue. Computer science is ironically not a science. It lives in the same axiomatic based world as mathematics and therefore things can be proven in computer science but not in science itself.
So this nomenclature issue is what’s confusing everyone. The op failed to identify that computer science isn’t actually a freaking science. Physics is a science but computer science isn’t.
So what is computer science? Sorry to say but it’s a math. I mean it’s all axioms and theorems. It’s technically math.
CS is a math in the same way algebra and geometry is math. Physics is a science and it is not a math. It’s a totally orthogonal comparison.
Your job as programmers is more like applied math. It’s completely orthogonal to the whole topic but People often get this mixed up. They start thinking that because programming is applied computer science then computer science itself is not a math.
Applied math ironically isn’t really math in the same way writing isn’t a pencil. Yes you use a pencil to write but they are not the same. Same thing with computer science and programming.
Asking here because it is mostly on-topic: This phrase is repeated often, but shouldn't it actually be, "In science, a hypothesis is either fundamentally verifiable or fundamentally falsifiable, but never both"? The two simply being the logical negation of each other.
"All swans are white" is fundamentally falsifiable (by seeing a black swan) but not verifiable, as you described.
"Black swans exist" is fundamentally verifiable (by seeing a black swan), but not falsifiable.
Science has a word encompasses a broad variety of definitions and practices. The philosophical question of the relationship of empiricism to truth (because fundamentally the question has more to do with the relationship between observations and deductions than science in itself) is a complex one and overall of little interest to actual practitioners of science. It can’t easily be subsumed in broad aphorisms.
I would hazard that most modern sciences - and physics especially - are nowadays mostly concerned about building models and the resulting predictions. The question then often becomes: does the tool I have built allow me to correctly predict how observations will unfold? The answer to which is often more shades of grey than simply yes or no.
Science is about measuring, quantifying and qualifying uncertainty.
https://news.ycombinator.com/item?id=41851265
If you want to learn more look up Karl popper. It’s his philosophy.
In response to the other sibling replies I’m basically talking about science as in the scientific method. What are the limits of the scientific method in terms of determining truth?
One thing that isn’t addressed is fundamentally limited accuracy and precision of observational instruments. This actually makes things not falsifiable as well but I don’t talk about this because it complicates everything.
Because science depends on the external world, and there might always be hidden variables that we are not considering, it can only give us extremely high confidence after we make repeated observations using different methods, but it cannot give us the absolute confidence that Math can give us.
Also, this example of faulty telescopes is actually really close to what actually happened in the history of astronomy. Stars were thought to have a visible radius that made them appear to be much larger than the Sun, which was considered evidence that the Sun was not a regular star.
Here's an interesting thing. Even high confidence can't be verified.
Let's say you examined 10 million swans and you think you observed all possible swans. But there's no way you can know whether or not the actual population is 10 billion trillion swans or a google swans.
If you observed 10 million swans and they are all white but those swans could only represent 1/99999999999999 of all possible swans. Then that means your observation is low confidence and there's no way whether we can verify what fraction of the population our sample size represents.
So actually high confidence is just an assumption. At a very technical level the confidence that science brings to the table is very very weak. We are making tons of assumptions and jumping to conclusions all the time.
This one is actually a funny statement. Not all assumptions are born equal :)
For example, distributed systems and networking are more like a physical science because they seek to make generalized learnings and theorems about real world systems.
The author’s last point around complexity theory also resonates because it demonstrates the value of designing experiments with real-world conditions like computing hardware speed and input sizes.
That’s not to discount the reality that mapping the model to reality is hard work that needs to be done.
[1] https://lamport.azurewebsites.net/tla/formal-methods-amazon....
The authors last point is basically like what applied math is to math. It’s applied computer science.
Empathetically speaking I’m sure it’s quite jarring for you when you read it.
A single math
One of these expressions doesn't make sense. So no, you cannot use "math" like "fruit".
An amusing thing about a hypothesis like "all swans are white" is that if you do want to go around making observations to support it you don't actually need to observe any swans.
"All swans are white" is logically equivalent to "All non-white things are not swans". Thus you can gather observational evidence for the hypothesis by finding non-white things and checking if they are swans.
My monitor is not white, and I see it is not a swan. I've just made an observation in support of "all swans are white". I can make hundreds of such observations without even leaving my house.
I feel sorry for all those other swan color researchers who had to trudge around slimy rivers and mucky wetlands checking the colors of swans.
I think I first saw this in a Martin Gardner book. It is amusing, but actually there has been quite a bit of serious work among logicians and philosophers over this [1] since the logic seems correct but intuitively it seems you shouldn't be able to research swan color by looking around at the furniture in your house.
The negation and the original statement can’t be proven. They can only be falsified.
The reason why you can’t prove things in science is because reality is unbounded so at any point in time in the future you may observe something that contradicts the hypothesis.
But I think there is also an etymological issue or something as well, which is causing additional confusion. Scientific theories aren’t proven of course, but they are proofed, in the same manner as when you pick up a breastplate from the blacksmith and note that it has a dent in it from where he shot it once. That’s the proof mark, the armor was tested by giving it a reasonably challenging test that is appropriate to the task it is intended for. Does this prove the armor is indestructible? No, of course not, as a physical device the armor has some finite limitations which could be overcome with enough gunpowder. But it is still reassuring.
Therefore I propose we clearly delineate between the two, by always spelling the logic thing with a ve and the “well, I tested it pretty hard and it didn’t break” thing with an f.
Newtonian physics was mostly mechanical engineering proof. It turns out electrical engineering, the study of fields and waves, that was a higher caliber. The standard model seems to be EE proof. But physicists are always constructing more energetic experiments.
- I proof the armor is solid
- That’s a mathematical prove.
“The armor has been proofed” doesn’t look so bad. “The armor has been proven” actually looks a tiny bit more awkward to me because it brings in too much of the math meaning.
Prove as a noun, though, I agree it is a little awkward.
But this is a request to change the language (where are those filed?) so I guess we will get used to it if it goes through.
> In science nothing can be proven.
Who are you referring to? Nobody has mentioned anything about proven. Your entire comment is focused on arguing against science being proofs, but nobody has said science is proofs.
OP said that scientific theories should "explain and predict" which they should. Those that don't should be discarded eventually (which they should). Why are your discussing mathematical proofs of science when nobody brought it up nor proposed that?
- In science nothing can be proven.
- In math things can be proven.
- computer science is not a science because you can prove things
- computer science is a kind of math because you can prove things
You guys don’t understand what math is and you don’t understand what science is and thus you guys are classifying incorrectly that computer science isn’t a math and they are making a completely invalid comparison with physics which is actually a science.
If you start with the premise that computer science is math, of course you'll reach the conclusion that computer science is math. And that's why you're so surprised that anyone else can reach any other conclusion. But the issue is in your premise - that's what you need to re-examine.
The math portions of computer science are math - and the non math portions are not. Your argument is equivalent to saying that Europe is defined by the counties in that continent using GMT - and concluding "Of course Italy isn't in Europe!".
Parts of Computer Science (the theoretical parts) sit in formal science just like logic and math do. But parts of CS like applied CS don't. All of the hardware design and software falls into applied CS and eventually slides into pure engineering.
But CS also is more amorphous than many other disciplines. Parts of it almost touch up against behavioral science with its subfield of linguistics, and syntax and semantics of language. And a failure of CS over the past 50 years has been the utter lack of progress in empirical data around human modeling of computation. We still don't have any empirical framework for evaluating what languages or modeling approaches are more efficient than others, or even what makes a more efficient programing language. As a result that is stuck in alchemy and cargo culting.
Models of computation and information theory begin to intersect with the natural sciences n the realm of physics. Physicists begin to push up against what is computable by nature in a given region of space. And Quantum computation begins to redefine what the physical bounds are on computation.
Don't begin by looking at what math is - if you do then the only thing possible to conclude is that it's math . An informal definition you could begin with might be "The theory and application of tools (ie formal cs) and models (ie applied cs) that predict and explain behavior related to Computation"
How do you model the real world via computation? What are the limits of computation? How do you implement computation?
Computer Science is the study of all aspects of computation.
The term is "theoretical computer science." Not just "computer science"
https://www.wikiwand.com/en/articles/Computer_science
https://www.wikiwand.com/en/articles/Theoretical_computer_sc...
The OP is making a claim on "theoretical computer science" NOT "computer science". Hence the title "What is theoretical computer science".
If you look at the wiki entry you will see that "Theoretical computer science" is highly mathematical and different from "computer science".
Honestly even I mis-used the term and this leads to tons of confusion. The naming of everything really changes the way people think and mixes everyone up. It's entirely a linguistic problem.
Consider this school of thought: My school burned down last week. The one where I went to elementary school.
A strawberry is not botanically a berry. A peanut is not a nut. A tomato is either a fruit or a vegetable. Nobody thinks this is a problem.
This is just language. Perhaps it's not actually a big deal that "Theoretical Computer Science" does not cleanly fall into your usual "Science" label?
What are you talking about? You're regurgitating points I already made as if I never made those points...
I literally said Computer science is NOT a science.
I said several times, it's a linguistic/nomenclature issue.
I don't think you're reading my responses. Are you trolling? If not please read over my responses more carefully.
Menawhile, you seem pretty hung up on the "In Science, nothing can be proven" part of a whole long argument as to why CS shouldn't be referred to as a science. Perhaps that distinction is not useful or relevant in context?
False. I said I acknowledge linguistic issues that can cause confusion. There is overlap but there is NO contradiction. There isn't a case where there are two conflicting definitions for a single term.
>Menawhile, you seem pretty hung up on the "In Science, nothing can be proven" part of a whole long argument as to why CS shouldn't be referred to as a science. Perhaps that distinction is not useful or relevant in context?
Meanwhile you seem hung up on me setting up clear and categorical distinctions as not useful or relevant.
Let me make it clear why your hang up doesn't make sense. The entire topic of this thread is an argument for "why CS isn't math." I am staying on topic and saying that CS IS a MATH and NOT a SCIENCE. Thus because I am on topic the distinction is ON context and HIGHLY relevant. You can disagree and state your points but saying my point isn't relevant is false.
It's not a valid argument. I literally stated the premise is false and stated the reason why, and you stated the reason is off topic as if I changed the topic .
But the point was that this entirely depends on one's definition of what the word "science" means - and that depends on the context and the language. I can say, for example, that math is science - simply equating "science" with "knowledge" and "research".
And I stated this in this thread several times. I defined what science is and I literally said, Computer Science isn't ACTUALLY a Science. It's incorrect terminology due to historical reasons. It's similar to greenland. Greenland isn't actually Green.
If you followed carefully what I wrote in this thread I defined what definition of science I'm using very very clearly and I ALSO stated why for the context of defining what "Theoretical Computer Science" using this definition has the most utility for the task at hand.
Look, not just you Koshkin, but everyone. This isn't even a thing that's really up for debate. Look at the wikipedia page for "theoretical computer science". The FIRST intro literally says it's the mathematical foundations for computation.
https://www.wikiwand.com/en/articles/Theoretical_computer_sc...
Additionally if you actually follow the wiki definition above of "theoretical computer science" all of the contents of that article are literally describing mathematics and nothing else. EVEN the introduction says it's math. You haven't commented on this point.
Also It's not a "my definition" it's more of a definition within a well known body of study called the philosophy of science.
Sources:
Some things can, some cannot (be either proven or shown to be false).
That fails as a scientific hypothesis on purely structural grounds, before you have made any observations. Scientific hypotheses have to explain something. It's not enough to say that all swans are white, you have to say why. "All swans are white" is an observation, not a (scientific) hypothesis.
An example of a legitimate scientific hypothesis is that all swans are white because being white provides swans with some benefit in terms of reproductive fitness (and then you have to go on to say what that benefit is). You can then go on to predict that there might be non-white swans, but that these are expected to be rare because evolutionary pressure would drive non-whiteness out of the gene pool. Or something like that. But "all swans are white" by itself is a non-starter as a scientific hypothesis.
Basically a hypothesis is a statement that can be true or false. That's it.
The reason I refer to science in this very technical way is because the we are tackling the problem of classification. We are asking the question what is computer science? So to answer the question we need to use very technical definitions where the boundaries of categorization are extremely clear.
Again, at a very technical level a hypothesis is simply a statement that is true or false.
> Basically a hypothesis is a statement that can be true or false. That's it.
No, a statement which can be true or false is just a proposition. The reason that we care about "why" is that a hypothesis has bearing on many falsifiable propositions. It's the difference between "the specific rock I dropped accelerated at 9.8 m/s^2" and Newton's law of universal gravitation.
No, that is a proposition, not a hypothesis.
And the requirement that hypotheses be explanatory has nothing to do with culture, it is the distinguishing feature of the scientific method. See: https://blog.rongarret.info/2024/03/a-clean-sheet-introducti...
https://www.sciencedirect.com/topics/mathematics/statistical....
When you cut through all the cultural and human stuff we place around the scientific method, in the end it is a statistics problem at the most technical level. Everything else makes it fuzzy and hard to define.
Then you made an assertion that a hypothesis "is a statement that can be true or false. That's it."
Now, you're asserting that a hypothesis "is defined by statistics". Never mind that humans did a bunch of science before statistics were developed, this is different than your prior statement ("true or false. That's it."), and you seem extremely confident in it.
You're acting as if you have certainty in a statement, but you did not arrive at it by a proof. You've claimed that only the falsifiability of a statement matter, not its explanatory structure, but your own statements about hypotheses are structural and definitional ("defined by statistics", "at the most technical level", "ignoring all the cultural stuff"). You've asserted that a hypothesis is falsifiable, and intrinsically statistical, but you bring no quantitative data in support of this.
I don't know what activity you're engaged in, but it doesn't seem like a rigorous and principled search for truth. And you seem to be more willing to preach about the importance of falsifiability than to apply that concept critically.
Yeah so? You can make a statement and the actuality of that statement is either true or false. But how you prove that statement to be true is NOT possible. That is my claim. I am also saying it is POSSIBLE to falsify the statement aka disprove it... All statements have this property.
>Now, you're asserting that a hypothesis "is defined by statistics". Never mind that humans did a bunch of science before statistics were developed, this is different than your prior statement ("true or false. That's it."), and you seem extremely confident in it.
Well you're using the "what came first argument" to say that the original scientific definition came before the statistical definition so it's more valid. I disagree.
Language emerges from concepts in attempt to explain things we only have vague understanding of. Concepts like Life and intelligence are ill defined and used for communication on topics we don't completely understand. It's useful to communicate this way but it's useful only because either we don't understand something completely or because we use it as a shortcut. Usually a new word starts off in this fuzzy state and as we understand things better the word takes on a more rigorous definition. Science started out without us understanding statistics, so that's why you have a lot of older definitions attached to it. The technical definition of hypothesis is part of mathematics. That is ultimately the most correct definition but it's not the definition with the most utility. If push comes to shove and we want to categorize a technical concept like computer science, then the technical definition is what matters more.
>You're acting as if you have certainty in a statement, but you did not arrive at it by a proof.
What. I never said this. You are entirely misunderstanding. I said statements can either be true or false. The proof of whether it's actually true or false is a separate issue. My original claim is that proving something true is impossible.
>You've claimed that only the falsifiability of a statement matter, not its explanatory structure, but your own statements about hypotheses are structural and definitional ("defined by statistics", "at the most technical level", "ignoring all the cultural stuff").
I didn't say only the falsifiability of a statement matters. I never said this. I said falsifying a statement is the only thing we logically have the ability to do. It still matters to do correlations and other types of things related to science but at a technical level we aren't proving anything. At a technical level things can only be falsified. This is not to say OTHER things don't matter. They do matter.
>You've asserted that a hypothesis is falsifiable, and intrinsically statistical, but you bring no quantitative data in support of this.
Did I not post a link to a resource stating this? This is Data supporting my point. If you want quantitative data for the English definition a word, I'm sorry but that's just not physically possible. English definitions cannot be quantified into numbers for any meaningful numerical analysis.
I know your question is just sort of rhetorical. Basically you think I'm being too pedantic and you're trying to illustrate a contradiction in my own logic. I don't deny it. In the end I'm using my own personal opinion here. But I share my opinion here because I believe if that the MAJORITY of people completely UNDERSTAND what I'm saying they will AGREE with me. That's all. But again opinion. And either way nothing can really be proven can it? Especially for english definitions.
>I don't know what activity you're engaged in, but it doesn't seem like a rigorous and principled search for truth. And you seem to be more willing to preach about the importance of falsifiability than to apply that concept critically.
What are you trying to say here? This is false. And it approaches the point of accusatory and a lie. I don't preach the importance of falsifiability. I am just saying that is the only possible technical thing we can do in terms of determining if something is true or false. I get technical because we ARE CATEGORIZING technical concepts and definitions so it's appropriate to DO THIS. If we are casually conversing or trying to understand concepts then of course we can revert to the more laid back way of communicating and fuzzy way of defining things.
But what's actually going on here is that we are determining whether or not a technical concept: "Theoretical computer science" is math or not? Such detailed and rigorous categorization REQUIRES the use of detailed and rigorous definitions.
It can also be "not even wrong."
A hypothesis is a statement that is TRUE or FALSE. And THIS is HOW it's defined by statistics.
>I'm not going to waste time debunking every half-baked idea you can come up with.
I'm sorry but this attitude is offensive and against the rules here. I can't participate in any further discussion with you because of this. Thank you for your time and good day.
I would say in physics it's also a population parameter. It's just sometimes we feel so confident about a single observation that we only need to take 1 sample.
>You may disagree, but I see statistics as a science, akin to physics
I don't disagree. This has been my entire point. I define statistics as the foundational formal definition of the scientific method.
Yes, they were. You started out by saying, "a hypothesis is a statement that can be true or false. That's it." But that isn't "it" as you yourself found it necessary to explain.
> I can't participate in any further discussion
That's fine, I'm writing this response for the benefit of others who might be reading this: not only are both of your claims wrong, they are transparently wrong. "Santa Claus lives at the North Pole" is a statement that can be either true or false (it happens to be false) but it doesn't have the same standing as a scientific hypothesis as, say, "the laws of physics are invariant under Galilean relativity." That happens to be false too, but it is not nearly as false as "Santa Claus lives at the North Pole." And neither of these has anything to do with statistics.
You clearly don't understand the first thing about how the scientific method actually works, starting with the fact that you cannot strip away "the cultural stuff." Science is a human endeavor. It is ultimately about accounting for our subjective experiences because that is all any of us have direct access to. This includes, but is not limited to, the fact that there seems to be this thing people do called "science", which has a bunch of interesting properties and turns out to be tremendously useful. Statistics are only a small part of that endeavor. An important part to be sure, but a small part nonetheless.
Meanwhile, before the moderator arrives, I'm placing this comment here to ask people to stop responding to him and aggravating the thread further. Thank you.
Please don’t aggrevate this further.
Either way please stop extending this thread.
you have been sufficiently approached, your points addressed, and multiple people have provided ample reasoning that expound on their assertions, adding context, nuance, historical, conventional, or otherwise.
all you have contributed to the over-reaching discussion is assertions (in some cases they come across as not fully thought out, as if the tape was not fully played), followed be an emphatic and repeated: "you're wrong!"
and for as much as you have claimed to strip away culture as an influence to the discussion, you have also managed to strip away important nuances between established words in our -- cultural -- expression here: proposition vs. hypothesis.
it appears that the position here is attempting to generally (and loosely) apply a statistical hypothesis as the internal world model for science at large, where in stats the word hypothesis is almost a binary operator evaluating to true or false (ie: Null Hypothesis), and functionally operates more like asserting a proposition over a data set, and then evaluating the data to see if it holds.
as a comment reader, while i appreciate the discussion, reducing everything to a statistical hypothesis and then telling people they are wrong when they show, not tell, there are important, established, agreed upon meanings, is not contributing in good faith, which i imagine is causing a lot of the aforementioned frustrations.
I was insulted go back and look at it.
If you want to discuss things with me, please do so in another thread. I welcome you to tell me I'm wrong as I will do the same if I disagree with you. Telling me I'm wrong is not an insult and it's the basis of truthful honest discussion. If you believe I'm wrong, tell me straight. Don't dance around it.
But it must also be useful. We don't do science just to enumerate trivial true statements, after all.
To be useful it needs to predict things.
And when it's falsified (say your hypothesis explained why swans are white, but you found a black one), it doesn't get discarded immediately. It's still useful until someone comes up with a better hypothesis that fits with white swans and the occasional black swan.
Sure it can be useful. Think of it like a mathematical theorem. What’s the point of the theorem unless it’s useful? Why would a book define a theorem if it wasn’t useful?
So theorems in math need to be useful. But such a quality is human and fuzzy in nature. What does it mean to be useful? And everyone has a different definition of useful. That’s why the definition of a theorem doesn’t include the term useful Even though generally speaking it’s a bit of a requirement if an author were to define a theorem in a book.
The definition for hypothesis that I use follows the exact same process. It is a rigorous technical definition that we are using for rigorous and detailed categorization of another term: “Theoretical computer science”.
Thus in the face of such a task I use the most rigorous definition of hypothesis available. I discard fuzzy terms like usefulness or expositions into “why” to determine categorization.
The statistical hypothesis which defines the term hypothesis in a very technical way. In fact, in statistics, hypothesis testing is basically the technical definition of the scientific method. Following this definition we can clearly see the boundaries of things more clearly.
Theoretical computer science does not involve hypothesis testing. It is mathematics because it involves axioms and theorems.
Similar to formalization where we determine the grammatical rules of a language in linguistics or formalization of a physical system to develop models for by using the statistical definition of hypothesis I am doing the same technical extraction here.
Sure informal definitions of hypothesis are useful but formal models are also useful and thus a formal model of science as defined by statistics is useful as well.
I am not denying alternative definition of hypothesis.
I am just saying that for the rigorous categorization of the term “theoretical computer science” we find that it doesn’t fit into the rigorous definition of the scientific method. There is a clear delineation here. If you want to use other definitions where “usefulness” and “explanations” are a factor then what literally stops knitting from being a science? Knitting can be useful and technical in terms composing fabric together…. why isn’t it a science?
You see the issue here and why technicality or formalization is needed? Intuitively we know knitting isn’t a science but we aren’t sure technically why… The technical definition of science elucidates the reason why knitting is not a science… because knitting doesn’t involve hypothesis testing. Plain and simple. We discard fuzzy terms like “usefulness” and it ultimately becomes clear why knitting isn’t a science.
The other reason why the statistical definition of hypothesis is useful is because it helps us delineate categories for terms where our intuition fails and becomes ambiguous. We aren’t sure where “theoretical computer science” fits into terms of science or mathematics. Using technical definitions we find that theoretical computer science is actually a math and not a science.
If we use informal definitions then nobody is sure what computer science is. The mind is confused thinking it’s both a science and a math at the same time and the op starts to use analogies in attempt to justify certain categorizations. Any time you use analogies as proof you hit a sort of failure because analogies don’t prove anything. You need to use definitions as proof.
Hence the need for formal definition's. Your philosophers definition of hypothesis is unfortunately too informal.
If you aren’t talking about definitions then one person has one set of symbols and the other has none. So they are still discussing separate things.
Engineering - Physics - Math
Computer Engineering - Computer Science
Notice that the second only has two steps? Engineering isn't really science, but there is a sort of science. Now one will be quick to point out that computer engineering does depend upon physics (and chemistry, and even a wee bit of biology and higher). But I think Computer Science is large enough in scope it contains true Computer Science, which is as much math as math is, but it also contains more real world test and verify parts of computing. Things that might be able to fit up under physics or chemistry, but which ended up being placed under computer science.
If we are talking a Turing machine, that is math (or something equivalent to math). If we are talking about how a compiler can optimize code by rewriting some things to be computational equivalent but to put operations in an order that most CPUs can run faster, that feels like we've stepped into science. We've overloaded the terminology and now have some linguistic debt that needs paying off.
I sometimes joke that my undergrad degree in Computer Science involved only a single class in Computer Science.
In theoretical computer science, design and analysis of algorithms is the study of algorithms as mathematical objects. The unfortunately named algorithm engineering is the science of algorithms. It deals with algorithms that are written in code and run on real computers. Among other things, it seeks to build models that can predict the performance of an algorithm without implementing and running it.
Then there is algorithmic economics (or whatever it's called today), which was a huge success for theoretical computer science. At least in some amoral sense. The microeconomic models it created enabled turning the internet into the ad-centric data-driven dystopia it currently is.
You don't define it this way in common parlance or even in articles. But you do need to heavily define it this way when categorizing things. If you don't do this you have a categorical mishmash where nothing is ever truly defined properly and filled with fuzzy meanings. See the word "entropy" there are at least 3 definitions for that word and these definitions confuse people and lead most people to not completely understand the concept of what entropy is EVEN at just an intuitive and fuzzy level.
I realize it appears that I'm being overly pedantic and inflexible but this is NOT the case.
To be flexible means you need to understand why language SHOULD NOT have rigid definitions in certain contexts but also WHY it should be extremely rigid and concrete in other contexts. You need BOTH. When it comes to categorization on what is "theoretical computer science" and other very technical topics we Need to have well defined categories and definitions.
The fuzziness of literature and poetry which remains open to interpretation has significantly lower utility in technical fields.
It's useful for categorization (which is the overall topic). For formalization of concepts. Formalization is always useful for technical concepts. Programming is one of those things that requires formal definitions.
It's probably less useful for common communication. But that's not what I'm referring to. Sure in communication we don't require technical definitions. I'm not arguing for whether MY definition has utility in a variety of contexts.
I'm simply saying for the rigorous categorization being performed by the OP on what "theoretical computer science" is.... he should ALSO use the rigorous definitions of the Categories themselves.
Perhaps you're talking about the split between Electrical Engineering and Computer Science? That one isn't universal as some departments only offer EECS and not CS as a major, but when CS on its own is offered, "hardware" courses tend to be about microarchitecture, with practical work done using simulators. You're not required to know much of anything about electronics. But there is no program I'm aware of where a person can do nothing but math and get a CS degree. You have to write and test code.
This isn't really true, is it? There are mathematical models that predict but do not explain the real world. The most glaring of them is the transmission of EM waves without a medium, and the particle/wave duality of matter. In the former case, there was a concerted attempt to prove existence of the medium (luminiferous aether) that failed and ended up being discarded - we accept now that no medium is required, but we don't know the physical process of how that works.
Methods for explaining why include Counterfactual inference and/or now quantum Causal interference.
All or some of quantum statistical mechanics, fluid dynamics, and quantum chaos intend to predict with lower error too
List of popular misconceptions and science > Science, technology, and mathematics : https://en.wikipedia.org/wiki/List_of_common_misconceptions :
> See also: Scientific misconceptions, Superseded theories in science, and List of topics characterized as pseudoscience
Allegory of the cave > See also,: https://en.wikipedia.org/wiki/Allegory_of_the_cave
The only true statement:
All models are wrong: https://en.wikipedia.org/wiki/All_models_are_wrong
Map–territory relation: https://en.wikipedia.org/wiki/Map%E2%80%93territory_relation :
> A frequent coda to "all models are wrong" is that "all models are wrong (but some are useful)," which emphasizes the proper framing of recognizing map–territory differences—that is, how and why they are important, what to do about them, and how to live with them properly. The point is not that all maps are useless; rather, the point is simply to maintain critical thinking about the discrepancies: whether or not they are either negligible or significant in each context, how to reduce them (thus iterating a map, or any other model, to become a better version of itself), and so on.
Maybe the issue is how he thinks about mathematics... He quotes Von Neuman saying:
> We should remember the warning of John von Neuman,e one of the greatest mathematicians and computer scientists of the 20th century, regarding the danger of mathematics driven solely by internal esthetics: “There is a grave danger that the subject will develop along the line of least resistance.”
But for example, there is an article in Quanta [0] about a recent proof in Number Theory (you cannot get more "mathematical" than that), and the guy who proved it said:
> “Mathematics is not just about proving theorems — it’s about a way to interact with reality, maybe.”
Which is in line with Von Neuman's quote, and with the spirit of what the author is saying.
So maybe a more accurate subtitle would be:
"Thinking of theoretical computer science as a mathematical formal system is harmful to the discipline."
[0] https://www.quantamagazine.org/big-advance-on-simple-soundin...
As Kant teaches us in A Critique of Pure Reason, mathematics is the cultivation and extension of intuitive intellectual tools. This puts it in natural opposition to philosophy (which deals with conceptual intellectual tools) and natural science (which deals with the empirical nature of the Actual world). None of them would be very useful without the others, but that does not mean that we should abandon the distinctions, imo.
That article is great, but I think the immediately preceding sentence is telling:
Earlier that year, his father had died, and Pasten found himself turning to math for comfort. “I found mathematics really helpful for that,” he said. “Mathematics is not just about…
I guess this points back to the eternal debate about if mathematical objects are invented or discovered. If they are discovered, then that would mean that there is an underlying truth/semantics behind the mathematical formalisms. So in that case mathematics studies and interacts with reality. Take for example Calculus and Newton and Leibniz [0] who invented/discovered calculus independently.
I will let you decide on what side of the debate you feel more comfortable :)
[0] https://en.m.wikipedia.org/wiki/Leibniz%E2%80%93Newton_calcu...
Regarding the article, I feel like there's some context missing, is this part of some ongoing debate about TCS? The piece abruptly ends.
One that comes to mind is the recent breakthroughs in AI which have caught theorists flat-footed. Sanjeev Arora and others openly admit we don't have a good theoretical understanding of the empirical successes of deep learning, how they are able to do the things they do with emergent phenomena, scaling effects, etc.
Scott Aaronson has also suggested that theoretical CS should be seen as analogous to theoretical physics.
On the other hand, I don't know if the argument could be abused to dismiss things like P vs NP as having no realistic scientific value. That would be the flip side of Vardi's argument. I do vaguely recall Aaronson in one of his blog posts or pdf essays* giving a more subtle argument about why P vs NP is central to computer science anyways, and I think that would be a slightly different position than either Vardi's or his reading of Widgerson's here.
*See the first several subsections about common Objections in pp 6-7 in: https://www.scottaaronson.com/papers/pnp.pdf
The argument seems to be that 1. a theoretical computer scientist is not a general mathematician and wouldn't be hired to a tenured math position ("sociological argument") and 2. treating it as a branch of math is "harmful" to theoretical computer science.
There are hints about what OP believes TCS is which isn't math, but I wonder why not make that an explicit argument — that would make it much easier to reason about and argue either for or against.
Without that, neither 1 nor 2 make a convincing case for anything: 1. a Linear Algebra expert might not get a position in a Statistics department either, and 2. it'd be useful to show some "harm" before you claim anything being "harmful". CS is also lucrative enough that it pays to have a dedicated faculty just for CS too (as in, it attracts students, contracts with external parties for a university, etc).
X = X + 1
What does von Neumann mean here? Why is it bad that it will develop along the line of least resistance? Does von Neumann advice that working on "harder" problems is more beneficial for TCS? Could not one argue that we should be solving away low hanging fruits first?
I am not sure if I am understanding von Neumann's quote nor this article properly. I would love to hear some simpler explanation (I am a new BSc. CS graduate).
If you look at new theories (let's say you are starting to study topology, or group theory) they start from some definitions/axioms that seem to come from "nowhere", but they are in fact a product of working and perfectioning a language for the intuitions that we have in mind. Once we set for the correct descriptions, then there are a lot of consequences and new results that come from interaction almost entirely with the formal system.
The interactions with the formal system is the path of least resistance.
The power of mathematics is that once you figure out a correct formalization of the intuitions, using just the formal system allows you to get a lot of information. That is why sometimes people identify mathematics with just the formal system.
Knuth thinking about algorithms led to all these research questions about combinatorics, that have turned out to be very interesting, but are much more messy and disjointed results.
.. mathematical ideas originate in empirics, although the genealogy is sometimes long and obscure. But, once they are so conceived, the subject begins to live a peculiar life of its own and is better compared to a creative one, governed by almost entirely aesthetical motivations, than to anything else and, in particular, to an empirical science. There is, however, a further point which, I believe, needs stressing.
As a mathematical discipline travels far from its empirical source, or still more, if it is a second and third generation only indirectly inspired by ideas coming from "reality," it is beset with very grave dangers. It becomes more and more purely aestheticizing more and more purely l'art pour l'art. This need not be bad, if the field is surrounded by correlated subjects, which still have closer empirical connections, or if the discipline is under the influence of men with an exceptionally well-developed taste. But there is a grave danger that the subject will develop along the line of least resistance, that the stream, so far from its source, will separate into a multitude of insignificant branches, and that the discipline will become a disorganized mass of details and complexities. In other words, at a great distance from its empirical source, or after much "abstract" inbreeding, a mathematical subject is in danger of degeneration. At the inception the style is usually classical; when it shows signs of becoming baroque, then the danger signal is up. It would be easy to give examples, to trace specific evolutions into the baroque and the very high baroque, but this, again, would be too technical.
In any event, whenever this stage is reached, the only remedy seems to me to be rejuvenating return to the source: the reinjection of more or less directly empirical ideas. I am convinced that this was a necessary condition to conserve the freshness and the vitality of the subject and that this will remain equally true in the future.
The definition of "theoretical physics" might have rapidly changed between 1900, 1920, 1940, and 1950--but certainly people who called themselves theoreticians remained mostly unchanged. Analyzing how everyone's definitions were changing gives a wealth of information about when and where breakthroughs were happening. 1919 and 1945 come to mind as such examples of when a theoretical field changed as a result of experiments [1][2].
Back to computing: Dijkstra told the story of attempting to put "Programmer" as his profession on his marriage certificate in 1957, and was rejected [3]. Clearly there are both pros and cons of using the sociological definition of a field. We all know programming existed before 1957, but the perception of it as a profession was so foreign that it wasn't allowed on an official document. It would've been impossible, apparently, where he lived to ponder about "What is programming?" if no one could BE a programmer. For that reason, we should probably be flexible and always be willing to discuss different definitions for every field so that we gain the benefits from multiple lines of reasoning.
[1] https://en.wikipedia.org/wiki/Eddington_experiment
[2] https://en.wikipedia.org/wiki/Trinity_(nuclear_test)
[3] https://amturing.acm.org/award_winners/dijkstra_1053701.cfm
Dr. Vardi's Second Law of Thermodynamics for boolean SAT and SMT (Satisfiability Modulo Theory) solvers is truly a marvel of interdisciplinary ambition. In his framework, computational entropy is said to increase with each transition of the Turing machine, as if bits themselves somehow carry thermodynamic weight. He posits that any algorithm—no matter how deterministic—gradually loses "information purity" as it executes, much like how heat dissipates in a closed system. His real stroke of genius lies in the idea that halting problems are not just undecidable, but thermodynamically unstable. According to Dr. Vardi, attempts to force a Turing machine into solving such problems inevitably lead to an "entropy singularity," where the machine's configuration becomes so probabilistically diffuse that it approaches the heat death of computation. This, he claims, is why brute-force methods become inefficient: they aren’t just computationally expensive, they are thermodynamically costly as well. Of course, there are skeptics who suggest that his theory might just be an elaborate metaphor stretched to breaking point—after all, it’s unclear if bits decay in quite the same way as particles in a particle accelerator.
From https://arxiv.org/pdf/1010.2067 "Manin and Marcolli [20] derived similar results in a broader context and studied phase transitions in those systems. Manin [18, 19] also outlined an ambitious program to treat the infinite runtimes one finds in undecidable problems as singularities to be removed through the process of renormalization. In a manner reminiscent of hunting for the proper definition of the “one-element field” F_un, he collected ideas from many different places and considered how they all touch on this central theme. While he mentioned a runtime cutoff as being analogous to an energy cutoff, the renormalizations he presented are uncomputable. In this paper, we take the log of the runtime as being analogous to the energy; the randomness described by Chaitin and Tadaki then arises as the infinite-temperature limit."
There is no such thing as the Second Law of Thermodynamics of a Turing Machine.
Unless! You turn the machine off. Then energy input equals zero, it becomes a closed system, and entropy kicks in.
My gripe with theoretical computer science was that if felt like a Newtonian physics level model of digital processes, while an equivalent of biology level models would be needed for/suited to most "real-life computing".
By the way, a lot of small CPU cores is what we use inside graphic cards. However they are not actors. They are very deterministic. The Newtonian physics model.
Incidentally, real-life computing depends quite a lot on the laws of the physics of the universe we live in. This has been known quite clearly since the theoretical discovery of quantum computing, with the resultant split of classical complexity theory and quantum complexity theory.
Morever, physics also determines what sort of devices you can make and with what performance. The real-life speed of solving NP-complete problems depends on the absolute and relative performance of transistors, CPUs, memories etc.
Hence, I submit that TCS has the same relationship to Physics as does Mechanical Engineering to Physics.
(See also how (much of) the math for General Relatively was developed without any application in mind.)
General Relativity much more natural than quantum mechanics. It was mostly created from a theoretical motivation. People were dragged towards quantum mechanics kicking and screaming and it took about 30 years to develop.
The fact that functions computable with such a machine is equivalent to functions computable in the lambda calculus and Herbrand general recursive functions is the remarkable results.
The fact that it can somehow be linked to an actual computing machines outside of logic is merely a happy accident.
Having said that you could think I disagree with Vardi but the truth is: I think the point he brings is just void of substance. That’s only of interest to people who like university politics and how departments hire. It’s of no impact to the field whatsoever. Why does it matter what is or isn’t semantically TCS and if it is or not mathematics? The problems will still be there the same.
https://justine.lol/sectorlisp2/
Also, the original paper on Lisp it's beauty itself. It's describing Lisp... in Lisp, recursively stating both (eval) and (apply). Magic.
I don't think that's a fair characterisation. Clearly, the SAT subset that SAT solvers solve efficiently is in P, so in that sense complexity theory "explains" it and even "predicts" it: clearly, there are subsets of SAT in P; some simple ones, such as 2SAT, can be easily described.
What complexity theory is yet to do is:
1. Either prove that the subset of SAT that can be solved efficiently covers all of SAT (in which case either P=NP or NP can be solved with such a low exponent that makes it tractable in practice) or identify and succinctly describe the subset of SAT that modern solvers solve efficiently, and it is in that sense that it doesn't yet "predict" it. But there are many open questions (including P vs NP) in complexity theory; that doesn't mean that the discipline is flawed. Many problems studied in complexity theory originate from practical questions, such as cryptography, and complexity theory does successfully and usefully explain and predict such real-world "phenomena".
2. Explain why that subset of SAT is prevalent in practice (making solvers "effective"). I'm not sure this is the job for complexity theory or any theoretical discipline for that matter (as opposed to empirical ones); after all theoretical computer science is meant to be theoretical. But there are mathematical disciplines (e.g. random graph theory) that do describe and even explain and predict mathematical structures that are more likely to arise in "nature".
> U.S. TCS has a quite narrower scope than European TCS, which I find unfortunate.
TCS is generally considered to have two primary subdisciplines: Theory of Computation (ToC, sometimes also referred to as "Theory A"), which is concerned with complexity and algorithms, and Theory of Programming (ToP, sometimes also referred to as "Theory B"), which is concerned with programming languages and type systems (and may be considered a sub-discipline of formal logic). Indeed, US ToC is more prominent in the US while ToP is more prominent in Europe, but I don't think some of the other CS sub-disciplines Moshe mentions (such as databases) are commonly considered theoretical computer science.
I don't have a position on the utility of describing theoretical computer science as a branch of mathematics or not doing so, but the very name "theoretical computer science" acknowledges that there are other sub-disciplines in computer science that are empirical rather than theoretical (such as studying the mistakes programmers empirically make, or the common causes for cascading failures, or studying side-channel attacks etc. etc.).
I don't think that those who consider TCS to be a branch of mathematics also consider all of CS to be a branch of mathematics or claim that theoretical computer science should aim to answer all interesting questions in computing, just as theoretical physics acknowledges the necessity of experimental physics and doesn't claim to cover everything physicists do.
As in theoretical physics and mathematics, results in theoretical computer science do sometimes explain and predict things we observe in the real world and sometimes not yet. But in all these cases, the theoretical subdisciplines aren't wholly subservient to the empirical ones or vice-versa.
As an example, the question of computability (decidability) isn't directly practical (as many decidable problems arent practically tractable), but the more practical question of tractability/complexity directly evolved from the study of computability.
Still waiting for theoretical physics to discard string theory, as it fails in predicting anything.
https://www.preposterousuniverse.com/podcast/2018/10/15/epis...
https://www.preposterousuniverse.com/podcast/2019/01/28/epis...
I love his “sociological sense”, and agree that at some level all these words are just words in language games that are defined with great diversity across the world’s academics, much less engineers and laypeople. But I also agree that there’s something worth defending in “computer science in its own right”, as I said above; that is, in turn, the core task of philosophy of science.
Of course I would expect him to push back on this description of the field because philosophy has lost all its street cred, but that would only encourage me to redouble my efforts. If it’s not empirical study of actual results, and it’s not mathematical study of intuitively-based theorems, what else is left?
With that said, I regard TCS as the study of discretized computation at scale. Or, more colloquially, what is the fastest way to do X, N times? This could be sorting, searching, indexing, drawing, tracking, balancing, storing, accessing, saving, reading, writing, whatever. The distinguishing characteristic is complexity analysis in time and space.
As a counterexample, I think cryptographic methods such as AES and RSA are much more pure math / number theory than TCS.
But asymptotics are heavily used, true. That is because often the theoretically interesting properties appear only when the inputs are huge (I'm sure this happens in other areas as well).
> The centrality of computing stems from the fact that it is a technology that has been changing the world for the past 80 years, ever since the British used early computing to change the tide of war in World War II.
I take issue with the idea hinted at here. Just like Algebra and other branches of mathematics were invented to deal with daily down-to-earth issues like accounting or farming, you'd be hard pressed to find a consensus that mathematics "aims to explain the real world".
The historical origin is very clear, but the train left the "real world" station pretty fast, "unreasonable effectiveness" notwithstanding. Am I to understand that because Enigma was broken using a physical machine, the field is bound to study physical reality? To me this feels as uncomfortable as to refer to astronomy as "telescope studies".
> I believe that thinking of TCS as a branch of mathematics is harmful to the discipline. [...] > Theories that fail at this “explain/predict” task would ultimately be discarded. Analogously, I’d argue that the role of TCS is to explain/predict real-life computing
Yeah, if you hired me to design harmful approaches, not in a year I would have come up with something as harmful as this.