Das Inverse Law strikes again

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Das Inverse Law strikes again
ity. Wary that whatever I might do will be inverted. Then the law will not be applied. So which vital
Last edited by Episcopus on Sat Mar 31, 2007 7:04 pm, edited 1 time in total.

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Re: Das Inverse Law strikes again
Or the wheel of Fortune:Episcopus wrote:It can take time to inverse fully, just like a windmill 
O Fortuna
velut luna
statu variabilis,
semper crescis
aut decrescis;
vita detestabilis
nunc obdurat
et tunc curat
ludo mentis aciem,
egestatem,
potestatem
dissolvit ut glaciem.
Sors immanis
et inanis,
rota tu volubilis,
status malus
Heraclitus: πάντα ῥεῖ.the denominator becomes the numerator after a certain period of time. Does it just apply to the life around here? Or is it universal?
William S. Annis — http://www.aoidoi.org/ — http://www.scholiastae.org/
τίς πατέρ' αἰνήσει εἰ μὴ κακοδαίμονες υἱοί;
τίς πατέρ' αἰνήσει εἰ μὴ κακοδαίμονες υἱοί;

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It seems you just label things without really knowing them entirely. You cannot say you don't like greek if you haven't studied it properly, or you can't say you just dislike her just because she looks like a clown (well you can, but you should try and know her)... We tend to hate and be afraid of the unknown.

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But when you calculate 4/2 this means the number of times 2 may be added to itself to be 4  times. 1/0 is the number of times 0 may be added to itself to equal 1. This is infinity, it can never be done.
tdomine, {quid dx ?
Yhevhe  I am ignorant but I could not have any enthusiasm for Greek  this is certain.
When das Inverse law you in the face hit, blame not me! You should have listened!
tdomine, {quid dx ?
Yhevhe  I am ignorant but I could not have any enthusiasm for Greek  this is certain.
When das Inverse law you in the face hit, blame not me! You should have listened!
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This is an interesting point Diane! But are you saying that if I have 2 apples in one hand and 2 in the other hand, that I could possibly have 5 in total?
Girls indeed have their free will, but in my experience (and perhaps it was my fault) often invert for themselves when something is not sound.
You do have the right to call me ignorant! This is because I am, and I acknowledge this.
OT: Where the truck is whiteoctave. Today however I became a 0.5l blood donor! Beeturque episcopi qui sanguinem vesanus postea factus receperit!
Girls indeed have their free will, but in my experience (and perhaps it was my fault) often invert for themselves when something is not sound.
You do have the right to call me ignorant! This is because I am, and I acknowledge this.
OT: Where the truck is whiteoctave. Today however I became a 0.5l blood donor! Beeturque episcopi qui sanguinem vesanus postea factus receperit!
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I'm not sure what sort of rap you listen(ed) to, Episcope, but I am reminded of a certain song once covered by Tupac Shakur called "Changes" cuius title, if not lyrics, is pertinentissimum to you...

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O Diane my dear lab partner! Should you ever see girls of these parts, you would not consider them people!
Das inverse Law can not physically turn the world upside down. As is probably obvious, it involves people only. By whom mathematics was created. So 1/x still stands.
Yes I have heard this song many times, it is difficult not to have; however I only wake up every morning wondering if I should take my protein shake, not whether I should do something very silly!
Das inverse Law can not physically turn the world upside down. As is probably obvious, it involves people only. By whom mathematics was created. So 1/x still stands.
Yes I have heard this song many times, it is difficult not to have; however I only wake up every morning wondering if I should take my protein shake, not whether I should do something very silly!
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This phenomenon relates to deficiencies in our ability to measure length, not in the number 5 itself. One can argue that it is impossible to perfectly define an "inch" because of limitations in technology and our incomplete understanding of extremely small distances (where our understanding of the basic fabric of the universe is limited) but if an inch can be defined, then there would be absolutely no doubt about what 5 inches would be.Diane wrote: Set out 5 apples and count them 10 times. You can get the same count every time.
Draw a line 5 inches long. Measure it 10 times, to an accuracy of 8/32 of an inch. Your ruler will be marked off in 16ths, so this means eyeballing the empty space between two lines in fourths. Are any of your measurements the same?
If your eyesight were blurry and you had difficulty seeing how many apples were on the table, it would not change the fact that there were 5 there.

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"Draw a line 5 inches long. Measure it 10 times, to an accuracy of 8/32 of an inch. Your ruler will be marked off in 16ths, so this means eyeballing the empty space between two lines in fourths. Are any of your measurements the same?" (Diane)
8/32" is 1/4", and 1/4 of 1/16" is 1/64". If you draw a line 5" long, it will always measure 5", as long as you use the same ruler (at the same temperature, if you're picky). That's because you won't be measuring the length of a line, but the distance between two points, and the human eye is very good at matching points (those of your ruler with those that mark the ends of the line).
If you try to draw a line 4 63/64" long using a ruler marked off in 16ths is when you get in trouble.
Your best bet is to always stick with the unit. How tall are you? One [Episcopus]. How wide is your house? One [width of your house]. Try inverting those.
8/32" is 1/4", and 1/4 of 1/16" is 1/64". If you draw a line 5" long, it will always measure 5", as long as you use the same ruler (at the same temperature, if you're picky). That's because you won't be measuring the length of a line, but the distance between two points, and the human eye is very good at matching points (those of your ruler with those that mark the ends of the line).
If you try to draw a line 4 63/64" long using a ruler marked off in 16ths is when you get in trouble.
Your best bet is to always stick with the unit. How tall are you? One [Episcopus]. How wide is your house? One [width of your house]. Try inverting those.

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1/Episcopus seems to enjoy the discussion of the apples, so 1/I'm sure he wants me to continue...
Diane,
You seem to be confusing several concepts: (1) mathematics, (2) our ability to interact with and understand our environment and (3) our ability to describe the environment.
The third I would call language and it is separate from mathematics. We can use different words to describe the same thing (mathematically) e.g. "first, second, third..." vs. "one, two, three..." The words a language uses to describe the mathematics is not the same as the mathematics itself. I could create my own language and use different words to describe similar mathematical concepts (I could even make the words for counting apples different than the words for counting oranges) but it doesn't change the mathematics.
The larger misunderstanding, though, comes from your suggestion that the simplifications we make to mathematics are somehow "different" from the more complex versions from which they derive.
Discrete mathematics is a simplification that we use to simplify what you would call continuous mathematics. The counting numbers (discrete) are a subset of the real numbers (continuous), but the number 5 is the same in both. A more interesting debate is how do you mathematically derive discrete numbers from a continuous set. An engineer, interested in building a structure or designing and electrical circuit, is happy to multiply the continuous function by the unit impulse function (named the Dirac delta function), but the mathematician, interested in the purity and beauty of mathematics will argue that the delta function is not a real function and he or she will go to great lengths to define it instead with limits of continuous functions, etc. until fundamentally the same result is achieved.
As far as the other points go, it must be remembered that we use mathematics to get work done, and for the sake of efficiency and speed we often simplify matters through rounding of other assumptions. If I cut of one Episcopus' apples in "half" I really haven't done exactly that. It may be 48.23...% to one side, part of the balance on the other side, and part on my knife. But that difference between my use of the term half and the actual exact meaning of half of the unit apple is a human simplification to allow us to function efficiently. It doesn't represent two different types of mathematics.
Likewise, of course, simpifications and rounding occur in computers. The fact that the computer cannot always exactly represent 5 does not mean that 5 does not exist, or that it has a different meaning to the computer, it just reflects a limitation of the computer (or a choice made by the programmer, depending upon the situation).
And finally, how can you reconsile these two statements:
Diane,
You seem to be confusing several concepts: (1) mathematics, (2) our ability to interact with and understand our environment and (3) our ability to describe the environment.
The third I would call language and it is separate from mathematics. We can use different words to describe the same thing (mathematically) e.g. "first, second, third..." vs. "one, two, three..." The words a language uses to describe the mathematics is not the same as the mathematics itself. I could create my own language and use different words to describe similar mathematical concepts (I could even make the words for counting apples different than the words for counting oranges) but it doesn't change the mathematics.
The larger misunderstanding, though, comes from your suggestion that the simplifications we make to mathematics are somehow "different" from the more complex versions from which they derive.
Discrete mathematics is a simplification that we use to simplify what you would call continuous mathematics. The counting numbers (discrete) are a subset of the real numbers (continuous), but the number 5 is the same in both. A more interesting debate is how do you mathematically derive discrete numbers from a continuous set. An engineer, interested in building a structure or designing and electrical circuit, is happy to multiply the continuous function by the unit impulse function (named the Dirac delta function), but the mathematician, interested in the purity and beauty of mathematics will argue that the delta function is not a real function and he or she will go to great lengths to define it instead with limits of continuous functions, etc. until fundamentally the same result is achieved.
As far as the other points go, it must be remembered that we use mathematics to get work done, and for the sake of efficiency and speed we often simplify matters through rounding of other assumptions. If I cut of one Episcopus' apples in "half" I really haven't done exactly that. It may be 48.23...% to one side, part of the balance on the other side, and part on my knife. But that difference between my use of the term half and the actual exact meaning of half of the unit apple is a human simplification to allow us to function efficiently. It doesn't represent two different types of mathematics.
Likewise, of course, simpifications and rounding occur in computers. The fact that the computer cannot always exactly represent 5 does not mean that 5 does not exist, or that it has a different meaning to the computer, it just reflects a limitation of the computer (or a choice made by the programmer, depending upon the situation).
And finally, how can you reconsile these two statements:
andDiane wrote:So, numbers are individuals outside of our control. They have their own rules to follow and completely ignore what we think they ought to do.
Diane wrote: But math is entirely the invention of the mind of man, and there is no particular reason for any of it to mimic the real world.

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"But math is entirely the invention of the mind of man, and there is no particular reason for any of it to mimic the real world." (Diane)
Man is real, and there is a very good reason for math to mimic the real world: Its application. And nothing that's real doesn't have a tolerance.
As edonelly said so eloquently, we shouldn't confuse math with measurements. A real meter is never going to be exactly 1 theoretic meter long, whether that theoretic meter is a fraction of the length of a meridian, the length of a kriptonite bar kept in Paris, or a fraction of the distance travelled by light in a second.
So, my dear Episcopus, before you start inverting your girlfriends make sure to get them decubitus first. You wouldn't want to get inverted yourself in the process.
Man is real, and there is a very good reason for math to mimic the real world: Its application. And nothing that's real doesn't have a tolerance.
As edonelly said so eloquently, we shouldn't confuse math with measurements. A real meter is never going to be exactly 1 theoretic meter long, whether that theoretic meter is a fraction of the length of a meridian, the length of a kriptonite bar kept in Paris, or a fraction of the distance travelled by light in a second.
So, my dear Episcopus, before you start inverting your girlfriends make sure to get them decubitus first. You wouldn't want to get inverted yourself in the process.