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In third grade parlance it is correct to say computers struggle with too many digits.

by symic 3y ago

mywittyname 3y ago
They don't "struggle". Computers exhibit definite behavior when a program attempts to store or operate on numbers that are too large for the allocated space. For integers, overflow behavior is pretty easy to understand.
- symic 3y ago
  Obviously I know this. As stated, in 3rd grade parlance it’s appropriate to say “they struggle”. Have you ever heard someone say, “I need a new computer; mine’s dying.”? This level of pedantic nitpicking is not appropriate for 3rd graders. I’ve heard professional programmers say that their computer struggles with compiling certain programs they are working on. Colloquialisms can be useful and they are ubiquitous.
  - musicale 3y ago
    It would be more accurate to say that calculating with very large integers or integer fractions with millions of digits can be slow on current computers - but it's still far beyond what humans can typically do without assistance. Million-digit numbers are absurdly large in terms of physical quantities, but can easily arise when one is enumerating possibilities, such as the number of ways that one could give out randomized phone numbers to everyone in a city. (That's the sort of explanation that my mathematically-inclined friends and I would have understood in grades 3-5, when we learned about integers, rational and irrational numbers, and basic probability/combinatorics, as well as simple algorithms for multi-digit arithmetic and conversion between integer and decimal fractions.) Factorial and exponential functions were (and are) fun to play with on calculators because of the large numbers you can generate; python and mathematica are even more fun of course. I think recent TI and Casio graphing calculators support python, though I don't know about their bignum support or memory limits.
    - symic 3y ago
      I think you missed that my comment was about explaining something to third graders or don’t understand what it means to explain something to people in that age group.
      - musicale 3y ago
        Even as a third grader I appreciated clarity and accuracy (as did my classmates.)
- burnished 3y ago
  Not the allocated space, the bit width of the ALU. Besides, your explanation doesn't add anything to the description of 'struggle' beyond 'in a normal and expected fashion'.
musicale 3y ago
Not sure what "struggle" or "too many" is supposed to mean, but my laptop (running Python in a Linux VM) handles million-digit numbers just fine >>> a=10**(1000000) >>> b=a//3 >>> len(str(b)) 1000000 Given that computers have calculated the value of Pi to more than 60 million digits , I think we can safely say that computers readily handle numbers with many digits.
- symic 3y ago
  A computer can’t display more digits than the number of particles in the observable universe. This is a finite number. As such it is correct to say that computers struggle if the number of digits is too large. While for practical uses modern computers don’t struggle with finite integers one normally encounters they do struggle with precision in certain circumstances. For 3rd graders I think it’s OK to introduce them to the concept that computers, like all devices, have limitations.
  - musicale 3y ago
    > A computer can’t display more digits than the number of particles in the observable universe. This is a finite number. As such it is correct to say that computers struggle if the number of digits is too large There are two sources of error here: 1. Your interpretation is essentially "computers struggle to complete tasks that are impossible for them to complete" - a meaningless tautology. At best it is "nothing scales infinitely" which perhaps is a bit more useful as a refutation for complaints that something "doesn't scale" in an unlimited fashion, but that doesn't seem to be the context here. 2. "Too large" is ambiguous. If it's "too large for computers to handle" then it devolves into the above meaningless tautology. However, a sensible and common interpretation would be to interpret "if <something> is too large" as "if <something> is very large" - but we know that computers can in fact handle numbers with huge digit counts (somewhere between 1 and 60+ million.) So the original statement is either a largely meaningless tautology or something that is misleading and/or incorrect. PP's criticism is valid.
    - symic 3y ago

In third grade parlance it is correct to say computers struggle with too many digits.

by symic 3y ago

In third grade parlance it is correct to say computers struggle with too many digits.

They don't "struggle". Computers exhibit definite behavior when a program attempts to store or operate on numbers that are too large for the allocated space. For integers, overflow behavior is pretty easy to understand.

symic 3y ago
Obviously I know this. As stated, in 3rd grade parlance it’s appropriate to say “they struggle”. Have you ever heard someone say, “I need a new computer; mine’s dying.”? This level of pedantic nitpicking is not appropriate for 3rd graders. I’ve heard professional programmers say that their computer struggles with compiling certain programs they are working on. Colloquialisms can be useful and they are ubiquitous.
- musicale 3y ago
  It would be more accurate to say that calculating with very large integers or integer fractions with millions of digits can be slow on current computers - but it's still far beyond what humans can typically do without assistance. Million-digit numbers are absurdly large in terms of physical quantities, but can easily arise when one is enumerating possibilities, such as the number of ways that one could give out randomized phone numbers to everyone in a city. (That's the sort of explanation that my mathematically-inclined friends and I would have understood in grades 3-5, when we learned about integers, rational and irrational numbers, and basic probability/combinatorics, as well as simple algorithms for multi-digit arithmetic and conversion between integer and decimal fractions.) Factorial and exponential functions were (and are) fun to play with on calculators because of the large numbers you can generate; python and mathematica are even more fun of course. I think recent TI and Casio graphing calculators support python, though I don't know about their bignum support or memory limits.
  - symic 3y ago
    I think you missed that my comment was about explaining something to third graders or don’t understand what it means to explain something to people in that age group.
    - musicale 3y ago
      Even as a third grader I appreciated clarity and accuracy (as did my classmates.)
burnished 3y ago
Not the allocated space, the bit width of the ALU. Besides, your explanation doesn't add anything to the description of 'struggle' beyond 'in a normal and expected fashion'.

musicale 3y ago

Not sure what "struggle" or "too many" is supposed to mean, but my laptop (running Python in a Linux VM) handles million-digit numbers just fine >>> a=10**(1000000) >>> b=a//3 >>> len(str(b)) 1000000 Given that computers have calculated the value of Pi to more than 60 million digits , I think we can safely say that computers readily handle numbers with many digits.

symic 3y ago
A computer can’t display more digits than the number of particles in the observable universe. This is a finite number. As such it is correct to say that computers struggle if the number of digits is too large. While for practical uses modern computers don’t struggle with finite integers one normally encounters they do struggle with precision in certain circumstances. For 3rd graders I think it’s OK to introduce them to the concept that computers, like all devices, have limitations.
- musicale 3y ago
  > A computer can’t display more digits than the number of particles in the observable universe. This is a finite number. As such it is correct to say that computers struggle if the number of digits is too large There are two sources of error here: 1. Your interpretation is essentially "computers struggle to complete tasks that are impossible for them to complete" - a meaningless tautology. At best it is "nothing scales infinitely" which perhaps is a bit more useful as a refutation for complaints that something "doesn't scale" in an unlimited fashion, but that doesn't seem to be the context here. 2. "Too large" is ambiguous. If it's "too large for computers to handle" then it devolves into the above meaningless tautology. However, a sensible and common interpretation would be to interpret "if <something> is too large" as "if <something> is very large" - but we know that computers can in fact handle numbers with huge digit counts (somewhere between 1 and 60+ million.) So the original statement is either a largely meaningless tautology or something that is misleading and/or incorrect. PP's criticism is valid.
  - symic 3y ago