EEVblog Electronics Community Forum
General => General Technical Chat => Topic started by: IanB on June 03, 2012, 06:28:06 pm
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I really hate to bury this in the religion thread, even though it seems relevant, so I'm giving it its own thread:
Do numbers EXIST? - Numberphile (https://www.youtube.com/watch?v=1EGDCh75SpQ#ws)
When I was a young child, I remember when I was first introduced to fractions in mathematics. I was told you could have numbers like one half, one quarter, and so on. You weren't only limited to one, two, three. With my head spinning, my immediate question was, "But, a half of what? You can't just have a half by itself, it has to be a half of something!" I guess I was born a nominalist.
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following your thoughts any number would be strange... 5 of what? 15 of what? ;)
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following your thoughts any number would be strange... 5 of what? 15 of what? ;)
Of course; but as best as I can recall my teacher at the time did not think to bring up that argument. Although within a short period I had considered that for myself and resolved the conundrum. It was fascinating to look back and see that at the time I had made the conceptual leap to whole numbers being abstract things, but fractions did not fit into my mental picture. I had to extend the picture before I could accept the idea that fractions were also numbers.
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Just think of numbers as apple pies. 5 (apple pies). 1/2 (of an apple pie). The A.P. theory of mathematics. Informative and tasty!
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Of course numbers do not exist as such they are only a way of describing things. How ever far you search the universe you will not find numbers in the wild, only in human's heads.
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So, can we say that a complex pie (a+bi) could be an apple pie that has a complex taste of apples and lemons at the same time?
-George
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I remember a long time ago in a maths degree where they taught for a whole semester the existance of numbers and that 1+1 is equals to 2.... Maybe.
So I think to find this answer you need to go in a maths degree. Or just google it ;)
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Well, I believe Math/Numbers is useful but its just an imagined set of rules that exists only on our minds.
It happens to work and we use it.
I often say Mathematics it's just like a game. Its the game with the most complex set of rules ever created.
There are things such as imaginary numbers, or when you do Fourier transforms: negative frequencies, which math requires to work, but when you pass from the math realm to the real world, you just have to drop it and use real numbers and positive frequencies when dimensioning your work.
Although I've accepted imaginary numbers for what they are quite easily, the negative frequencies really puzzle me.
I don't even see a need for them, but for imaginary numbers I do. Also, frequency is a measurement of the rate of something on the real world, its not purely a concept like a number.
A signal/wave/event that repeats every second has a frequency of 1 Hz, but what the hell is -1 Hz (minus one hertz)?!
Its still one time a second. How does it distinguish from the positive 1 Hz?
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but what the hell is -1 Hz (minus one hertz)?!
Its still one time a second. How does it distinguish from the positive 1 Hz?
It exists, and can practically be used relatively.
Like -2 liters per 100km.
Previous: 10 liters per 100km
After repair: 8 liters per 100km
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So is the square root of -1 an imaginary imaginary number?
There is also evidence that binary is way older than computers. Who ever imagined that one? Some guy with no fingers or toes? I would imagine hexadecimal comes from down south where kids have extra fingers and toes, and octal maybe the same where some kids have missing fingers and toes. (Maybe some clumsy shop teacher) This is a good question for Tom Leher!
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Who cares :)
There are so many levels on which you can confuse yourself.
Numbers are just like languages - a convention used to exchange/store/process information. The convention has changed over years and will keep changing as needs arise.
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If you have 3.14159etc pies, you have pi pies?
Pi Is (still) Wrong. (https://www.youtube.com/watch?v=jG7vhMMXagQ#)
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Numbers are the multiplier. The other element you need are units. You can have 2½ apples or 5 apple-halves. Without number units are meaningless too. Can you have a millimetre or a litre, or for those less advanced civilisations a mile or a gallon?
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this is what happen when you complicate thing, and to obsessed with our "visual" senses". number is a "concept" an intangible one. and it only apply/connect to certain "tangible matter" (or other intangible matter/concept/system/space/domain etc), it cannot apply by itself. just like "Feeling", feeling or what?. that person is beautiful. what is "beauty" can you see it? even the very letters you type/see here. where is "A", "B" etc? can you show? no, but its there, it represents something else. thats how we communicate.
now... we know (and believe solely) that 1+1=2, what is N/0? and why it is called "singularity"? not "plurality"? is our mathematical system perfect?... food for thought ;)
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Most people don't hit the "abstraction" wall until introduced to "imaginary" numbers, which are no more imaginary than "real" numbers. Just not as tightly tied to anything tangible.
Now, don't forget that there are a lot more irrational numbers (uncountable infinite) than there are rational numbers (countably infinite.) That was the bit that caused me to do a double-take...
And recently, via cryptography, there's the whole "modular arithmetic" field. Neat stuff.