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#21
07-07-2006, 06:48 PM
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Re: Base 10 Number System Question
[ QUOTE ]
[ QUOTE ] all computer people think in Base-16. [/ QUOTE ] This isn't true at all. Almost no "computer people" think in base 16. They understand it and can easily convert from base 16 to 10 or to 2 but they don't think in base 16. Trying to teach you children to do arithmetic in base 16 would just confuse them and waste their time when they could be learning much more useful information. [/ QUOTE ] Agreed. Broken down to the basic idea, you're basically teaching them to convert between number systems faster. I don't see how this is different than temperature or distance conversions. If you introduce number systems instead, having them work out the squares of 1-10 up to 10-15 powers, show them how certain systems repeat themselves in nature (Fibonacci and rabbits/plants/seashells etc.) Don't turn them into calculators, please. Just a view from a late 20's fella with one of his favorite childhood memories being the discovery of an algebra text in the third grade, and basically not being hindered by the "You're 8 years old, you shouldn't be doing polynomials. Go play with action figures instead." 
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#25
07-08-2006, 03:56 AM
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Re: Base 10 Number System Question
[ QUOTE ]
[ QUOTE ] all computer people think in Base-16. [/ QUOTE ] This isn't true at all. Almost no "computer people" think in base 16. They understand it and can easily convert from base 16 to 10 or to 2 but they don't think in base 16. Trying to teach you children to do arithmetic in base 16 would just confuse them and waste their time when they could be learning much more useful information. [/ QUOTE ] Ya, us computer types definitely don't think in Base-16. We do think in base 16 for a few specific things... take a bitfield, for example. You have a sequence of 32-bits (0/1)... each represents something that is turned on or off. If I said: Bitfield = 1234567890 It's not too easy to quickly convert to: 32 Bits = 1001001100101100000001011010010 But, if you had the base-16 representation of 0x499602D2 You would be able to quickly break it down quickly as: 4 = 0100 9 = 1001 9 = 1001 6 = 0110 0 = 0000 2 = 0010 D = 1101 2 = 0010 And, now you can quickly see the bits that are turned on and off. This is why Hex is an important representation for computer types. But, we certainly don't think in it when it comes to math. Maybe there are some freakish computer geeks that do, but neither I nor any of my colleages do. -RMJ
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#26
07-08-2006, 04:03 AM
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Re: Base 10 Number System Question
Binary has little character. Literally.
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#27
07-08-2006, 07:42 AM
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Re: Base 10 Number System Question
[ QUOTE ]
3) Base X refers to a number system with X digits. So a binary or base 2 system has 2 digits (0,1) and the "regular" number system is base 10 (0,1,2,3,4,5,6,7,8,9) [/ QUOTE ] Not quite. Base X refers to a number system where each place is worth X times the place to its right. There is a difference because it is possible to have number systems with negative or complex bases.
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#28
07-08-2006, 01:38 PM
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Re: Base 10 Number System Question
[ QUOTE ]
[ QUOTE ] 3) Base X refers to a number system with X digits. So a binary or base 2 system has 2 digits (0,1) and the "regular" number system is base 10 (0,1,2,3,4,5,6,7,8,9) [/ QUOTE ] Not quite. Base X refers to a number system where each place is worth X times the place to its right. There is a difference because it is possible to have number systems with negative or complex bases. [/ QUOTE ] Wiki on Radix [ QUOTE ] In mathematical numeral systems, the base or radix is usually the number of various unique digits, including zero, that a positional number system uses to represent numbers in a given counting system. [/ QUOTE ]
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#29
07-08-2006, 05:28 PM
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Re: Base 10 Number System Question
[ QUOTE ]
[ QUOTE ] all computer people think in Base-16. [/ QUOTE ] This isn't true at all. Almost no "computer people" think in base 16. They understand it and can easily convert from base 16 to 10 or to 2 but they don't think in base 16. Trying to teach you children to do arithmetic in base 16 would just confuse them and waste their time when they could be learning much more useful information. [/ QUOTE ] If you are an app programmer, or are limited to Java or something, you probably do not need to think in Base 16. If you actually work with the hardware you do. Not the same way you think about decimal on an every day basis, because you are more focused on shifts and masks and stuff. That's not the stuff I want my kid to know. I just want a higher base than 10, I choose hex because it's around. Most of you are missing my point, which is: (1) Children are information sponges. They learn super-quick. This will not be confusing, will blend into other lessons, and once known, will be super-useful. (2) The ability to work with large numbers in your head is super-useful, because you don't always have a calculator. The bottleneck is number of digits. I can multiply 3-digit numbers by each other in my head but have trouble with 4. You can do multiplications in your head in hex that you couldn't dream about doing in decimal, because it requires less digits.
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#30
07-08-2006, 05:36 PM
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Re: Base 10 Number System Question
[ QUOTE ]
[ It's not impossible, but I'm wondering if it is actually more efficient. Most, if not all, modern mathematical theories were founded in decimal, so translating those theories to hex would likely be necessary to complete work in hex. Since you've so kindly introduced the analogy of language, I opt to introduce the concept of fluency in a language. Being truly fluent in a language means that you think fluently in that language, which appears to be what you want. But consider the extreme example of you being fluent in English and Japanese with the rest of the world being fluent only in Japanese. It would appear that, on the surface, there is not much benefit to using English. Suppose (and this is purely hypothetical, since I'm not fluent in Japanese) English is a more complex language that allows for superior methods of thinking (like your hex). Still, in an all-Japanese world, translating to English before completing work in Japanese doesn't make much sense. You might as well just complete the work in Japanese. My point is that fluency in English will not benefit you in terms of fluency in Japanese. Thus, I think that fluency in decimal is more important than fluency in hex. If you do indeed train your children in hex, then I should hope that either you are a hex genius or you know where to find one. Much of my own learning in math and science was accomplished from reading books, all of which used decimal notation. [/ QUOTE ] There have been studies that bilinguals are smarter, based on the bilingualism. There's a myth that sometimes pops up, that there's only so much information in your head you can store, but this simply isn't true. Knowledge begets knowledge. When I took Spanish classes in college, I started looking at some words in English from a different perspective. It's hard to describe, but hopefully you know what I mean. Also, as far as proofs, in all the math classes I've taken beyond simple algebra, I've never really seen much that depends on decimal. Usually there's a constant k that could be in any base.
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