Can someone be a good data scientist without knowing Calculus?
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A couple of things related to the referenced article: 1. the article is from 2014; world seems to be going the same even if high school curriculum didn't change in the last 10 years. Besides article was referring only to US and high-school curricula vary from place to place. 2. the author wants to introduce both statistics and computer science. As most of us, programming practitioners, would agree, there is no real "computer science"; just a bit of craftsmanship and flavor of the day buzzword(s) - structured, object-oriented, functional, agile, extreme, cloud, as-a-service, etc. In the interest of full disclosure, I hold one of those "computer science" degrees. Uni taught me many things one of them being that computers are not (yet) a science. One more example that maybe we shouldn't give much importance to journalists.
Mircea
Mircea Neacsu wrote:
computers are not (yet) a science.
Computer science is not programming. Computer science deals with algorithms, complexity, etc., and has a firm basis in mathematics. Programming, on the other hand...
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows. -- 6079 Smith W.
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Mircea Neacsu wrote:
computers are not (yet) a science.
Computer science is not programming. Computer science deals with algorithms, complexity, etc., and has a firm basis in mathematics. Programming, on the other hand...
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows. -- 6079 Smith W.
While I see your point, allow me to argue that the vast majority of graduates of "computer science" programs will not practice the Computer Science you are talking about. Also I don't see how Computer Science would be taught at high school level. Nor do I see why it should.
Mircea
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While I see your point, allow me to argue that the vast majority of graduates of "computer science" programs will not practice the Computer Science you are talking about. Also I don't see how Computer Science would be taught at high school level. Nor do I see why it should.
Mircea
Mircea Neacsu wrote:
the vast majority of graduates of "computer science" programs will not practice the Computer Science you are talking about
Agreed. However, a competent programmer will have been exposed to the product of computer science. He/she/it will know algorithms, have some idea of their complexity (time, memory, etc.), and have an idea of when they should be used.
Mircea Neacsu wrote:
Also I don't see how Computer Science would be taught at high school level.
Schools could use it to replace Latin as a subject that requires logic and discipline but is totally useless in the modern world. :)
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows. -- 6079 Smith W.
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Mircea Neacsu wrote:
the vast majority of graduates of "computer science" programs will not practice the Computer Science you are talking about
Agreed. However, a competent programmer will have been exposed to the product of computer science. He/she/it will know algorithms, have some idea of their complexity (time, memory, etc.), and have an idea of when they should be used.
Mircea Neacsu wrote:
Also I don't see how Computer Science would be taught at high school level.
Schools could use it to replace Latin as a subject that requires logic and discipline but is totally useless in the modern world. :)
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows. -- 6079 Smith W.
Daniel Pfeffer wrote:
Schools could use it to replace Latin
De gustibus non disputandum est :D
Mircea
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No. Calculus exposes one to the ideas of trends, maxima, minima, limits, etc. All important concepts in data science.
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows. -- 6079 Smith W.
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Amarnath S wrote:
Akin to trying to understand Shakespeare's works
Not at all. First of course and most important, Shakespeare's works are written in Old English. Which is difficult to understand even for someone that does understand modern english. And of course one doesn't need to be able to parse an english statement to communicate in english. There is also additional contextual information in Shakespeare that one needs to understand which has nothing to do with grammar. Certainly someone who wants to become a university professor specializing in Shakespeare is going to need knowledge in general history, history of the theater and history of that era. Not mention they better know who Bacon is. And that of course has nothing to do with grammar.
Am not familiar with any other English author than Shakespeare. Just meant that a knowledge of grammar - verb, noun, adjective, subject, object, preposition, etc. is needed for proper understanding of some long sentences or simple poems. I regularly read long sentences in Sanskrit, Kannada, Tamil, where there is a prescribed method of comprehending a sentence, based on grammar. Without which the sentence can sometimes mean exactly the opposite. In data science also, without proper understanding of calculus principles, methods like gradient descent will only be partially understood. Optimization methods are predominantly calculus based.
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Obviously, Statistics is the basis of Data Science, and one must know Calculus to understand Statistics at a deep level. Should We Stop Teaching Calculus In High School?[^]
Define calculus. I don't understand why double integrals are a required part of doing science. Do I really need to know Euler projections to be able to reason about and collect data? Or, how to formulate arguments for and against the calculation of an area, bounded by formula that contains i. None of this has made me a better scientist. Doing the legwork and chugging along until I gather enough high quality data, that's what made me a scientist.
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Define calculus. I don't understand why double integrals are a required part of doing science. Do I really need to know Euler projections to be able to reason about and collect data? Or, how to formulate arguments for and against the calculation of an area, bounded by formula that contains i. None of this has made me a better scientist. Doing the legwork and chugging along until I gather enough high quality data, that's what made me a scientist.
I think it's good to have some understanding of the maths which can be a tool in helping to show patterns in data - but in the end it still requires, or did require until the advent of AI, a human eye/brain/experience to be able to see patterns. Maths is not my strong point and I used to work as a production analyst with medical data - I was able to spot trends in data that some of the more mathematically competent scientists were not able to spot because I knew how to plot the data in graphs and interpret the "story" the graph was telling. Plotting data in graphs is something of a skill in itself as, depending on the choice of graph, trends can be exposed to the eye that even sometimes advanced statisticians cannot see in the raw figures.
“That which can be asserted without evidence, can be dismissed without evidence.”
― Christopher Hitchens
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I think it's good to have some understanding of the maths which can be a tool in helping to show patterns in data - but in the end it still requires, or did require until the advent of AI, a human eye/brain/experience to be able to see patterns. Maths is not my strong point and I used to work as a production analyst with medical data - I was able to spot trends in data that some of the more mathematically competent scientists were not able to spot because I knew how to plot the data in graphs and interpret the "story" the graph was telling. Plotting data in graphs is something of a skill in itself as, depending on the choice of graph, trends can be exposed to the eye that even sometimes advanced statisticians cannot see in the raw figures.
“That which can be asserted without evidence, can be dismissed without evidence.”
― Christopher Hitchens
Oh, we're talking about maths. I see, I agree with that notion 100%. It's probably lost in translation, but the difference between discrete calculus and theoretical calculus are like day and night. Calculus refers to theoretical calculus, no exceptions. Or else my former professor will rise from the grave and fail me from beyond, just to spite me.
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Obviously, Statistics is the basis of Data Science, and one must know Calculus to understand Statistics at a deep level. Should We Stop Teaching Calculus In High School?[^]
Doesn't that assertion confuse statistics (data we have) with probability (data we should have got if it followed the rules) ? Calculus follows the latter idea of `simple rules will predict complex data`.:rose:
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Amarnath S wrote:
Akin to trying to understand Shakespeare's works
Not at all. First of course and most important, Shakespeare's works are written in Old English. Which is difficult to understand even for someone that does understand modern english. And of course one doesn't need to be able to parse an english statement to communicate in english. There is also additional contextual information in Shakespeare that one needs to understand which has nothing to do with grammar. Certainly someone who wants to become a university professor specializing in Shakespeare is going to need knowledge in general history, history of the theater and history of that era. Not mention they better know who Bacon is. And that of course has nothing to do with grammar.
jschell wrote:
First of course and most important, Shakespeare's works are written in Old English.
As an aside, and it kind of illustrates how everything evolves, including science and mathematics, Shakespeare isn't really written in particularly old English. Elizabethan English, yes, but if you read some Chaucer, which is written in older (middle) English than Shakespeare, suddenly old Will's (modern English, in reality) works look a lot more modern and accessible, and you can get a real taste of old English by reading, say, the poem "Beowulf", which looks at first sight not entirely unlike German but with some unfamiliar characters, the most obvious being the thorn which is pronounced "th" and gave rise to the use of "Ye" as in "Ye olde inne".
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Obviously, Statistics is the basis of Data Science, and one must know Calculus to understand Statistics at a deep level. Should We Stop Teaching Calculus In High School?[^]
it seems you have the answer to your own question .
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Amarnath S wrote:
Akin to trying to understand Shakespeare's works
Not at all. First of course and most important, Shakespeare's works are written in Old English. Which is difficult to understand even for someone that does understand modern english. And of course one doesn't need to be able to parse an english statement to communicate in english. There is also additional contextual information in Shakespeare that one needs to understand which has nothing to do with grammar. Certainly someone who wants to become a university professor specializing in Shakespeare is going to need knowledge in general history, history of the theater and history of that era. Not mention they better know who Bacon is. And that of course has nothing to do with grammar.
> Shakespeare's works are written in Old English Shakespeare's works are written in Early Modern English http://www.shakespeare-online.com/biography/shakespearelanguage.html 🤓 Sorry to be pedantic, but there it is.
Time is the differentiation of eternity devised by man to measure the passage of human events. - Manly P. Hall Mark Just another cog in the wheel
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Am not familiar with any other English author than Shakespeare. Just meant that a knowledge of grammar - verb, noun, adjective, subject, object, preposition, etc. is needed for proper understanding of some long sentences or simple poems. I regularly read long sentences in Sanskrit, Kannada, Tamil, where there is a prescribed method of comprehending a sentence, based on grammar. Without which the sentence can sometimes mean exactly the opposite. In data science also, without proper understanding of calculus principles, methods like gradient descent will only be partially understood. Optimization methods are predominantly calculus based.
Amarnath S wrote:
In data science also, without proper understanding of calculus principles
Yes. Unfortunately there is a large disconnect between what the OP author posted (verbiage) and the link that they added as a reference. So as to the verbiage and only that your statement is very valid. For the link it says nothing at all about Data Science but it does comment on the need for Calculus (or not.)
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Am not familiar with any other English author than Shakespeare. Just meant that a knowledge of grammar - verb, noun, adjective, subject, object, preposition, etc. is needed for proper understanding of some long sentences or simple poems. I regularly read long sentences in Sanskrit, Kannada, Tamil, where there is a prescribed method of comprehending a sentence, based on grammar. Without which the sentence can sometimes mean exactly the opposite. In data science also, without proper understanding of calculus principles, methods like gradient descent will only be partially understood. Optimization methods are predominantly calculus based.
Amarnath S wrote:
the sentence can sometimes mean exactly the opposite.
You don't say.
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I never learned calculus. I had a semester of pre-calculus in college, but it was primarily trigonometry and I only remember that I took it. I also had a semester of statistics, which has been more useful. Discrete math and Finite math were also required for CS majors. But I wouldn't call myself a data scientist either. I like working with data and doing some light data analysis, but others are surely better at the heavy stuff than I. Even if I had learned calculus forty years ago, I wouldn't remember it now unless I had been using it all that time, so it wouldn't help very much, I'd have to re-learn it. "A man's got to know his limitations." -- Harry Callahan P.S. Most high school graduates do not need calculus. Or trigonometry. Or Algebra 2. Or geometry. When I graduated high school I had not yet decided to go into software development.
PIEBALDconsult wrote:
P.S. Most high school graduates do not need calculus. Or trigonometry. Or Algebra 2. Or geometry.
But then one can suppose why high school at all? For example I doubt I really need to know what a verb is. Certainly don't need to figure that out for work. I also don't need to know about the Russian revolution. I don't need to know about Freud. (Not convinced anyone should know about some of that nonsense.) I don't need to simulate erosion in a stream bed. I certainly don't need to know about running around a field collecting bugs with a net. Do I really need to know and be tested on the battles of the civil war? How many hours should I spend being taught the structure of the US government? Did I really need to know how to create a blueprint on a drafting table? Did I really need to dissect a frog? Did I really need to figure out the impact of solids on freezing water? Then there is the problem of if I don't learn any of that what happens when I finally decide to be a programmer, historian, author, politician, doctor, electrician, biologist, etc? Do I then start learning the above? How do I even know what any of those occupations might even be if I didn't learn some of the basics involved in it? So if I don't really need to know any of that I don't need to go to school as long as I did. So what do I spend my time doing instead? Crawling around in a loom at a factory to free up problems doesn't sound like much fun (which is what at least some young children were doing before mandatory schooling.)
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PIEBALDconsult wrote:
P.S. Most high school graduates do not need calculus. Or trigonometry. Or Algebra 2. Or geometry.
But then one can suppose why high school at all? For example I doubt I really need to know what a verb is. Certainly don't need to figure that out for work. I also don't need to know about the Russian revolution. I don't need to know about Freud. (Not convinced anyone should know about some of that nonsense.) I don't need to simulate erosion in a stream bed. I certainly don't need to know about running around a field collecting bugs with a net. Do I really need to know and be tested on the battles of the civil war? How many hours should I spend being taught the structure of the US government? Did I really need to know how to create a blueprint on a drafting table? Did I really need to dissect a frog? Did I really need to figure out the impact of solids on freezing water? Then there is the problem of if I don't learn any of that what happens when I finally decide to be a programmer, historian, author, politician, doctor, electrician, biologist, etc? Do I then start learning the above? How do I even know what any of those occupations might even be if I didn't learn some of the basics involved in it? So if I don't really need to know any of that I don't need to go to school as long as I did. So what do I spend my time doing instead? Crawling around in a loom at a factory to free up problems doesn't sound like much fun (which is what at least some young children were doing before mandatory schooling.)
jschell wrote:
one can suppose why high school at all
Yeah, I almost mentioned that. Most people don't need more than a sixth or eighth grade education.
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Mircea Neacsu wrote:
computers are not (yet) a science.
Computer science is not programming. Computer science deals with algorithms, complexity, etc., and has a firm basis in mathematics. Programming, on the other hand...
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows. -- 6079 Smith W.
Daniel Pfeffer wrote:
Computer science deals with algorithms, complexity, etc.
And the techniques used for creating computers. Time-sharing, data storage, etc. Not so much applying computers to different domains.
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jschell wrote:
one can suppose why high school at all
Yeah, I almost mentioned that. Most people don't need more than a sixth or eighth grade education.
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sixth or eighth grade education.
Like one Jethro Bodine, he wanted to be a brain surgeon or a 'double naught spy' or a movie producer with the 6th grade education!
"the debugger doesn't tell me anything because this code compiles just fine" - random QA comment "Facebook is where you tell lies to your friends. Twitter is where you tell the truth to strangers." - chriselst "I don't drink any more... then again, I don't drink any less." - Mike Mullikins uncle
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Obviously, Statistics is the basis of Data Science, and one must know Calculus to understand Statistics at a deep level. Should We Stop Teaching Calculus In High School?[^]
IF COVID taught us ANYTHING is that scientist rarely agree when they don't want to agree. What I mean is this. From the first data that the CDC posted many data scientists tracked projections and posted the results to have nearly everyone say they were wrong. I watched at virologists who had 1000's of case studies under their belts get slammed as quacks. I too ran the same calculations and came to the same conclusions and lost respect for people who just discounted the math out of hand. Roll forward to just this year when the real final numbers came out and nearly all of the people who were mocked and dismissed were right. The numbers told us then and tell us the same thing today the difference is now people agree. We assumed these statistics, from the majority, were from people, with a high understanding of the math. Turns out the majority were wrong and the few got it right.... So the question to me is Does knowing Calculus make you a good data scientist? NO emphatically not.