Division By Zero

[Captain McBain]

Still, it doesn't mean that Data would be the best source, though. He doesn't know everything, he just assimilates knowledge faster than humans. There's no reason to think the concepts of 24th century mathematics would be above Riker's head, or Worf's, for that matter.

Yes, it's certainly possible that Riker and Worf are mathematically gifted. But if you had a choice to go to either Data or Riker and Worf for math assistance, whom would you choose? It'd be like me choosing an $8 calculator to try and do complex equations rather than seeking help from various websites, etc.

Data doesn't know everything, but it seems impossible to me that he wouldn't understand calculus. If there are people living today who are experts in calculus, I don't know how Data couldn't be. Especially since calculus is still very much revelant in the 24th century.

 

[Pavonis]

So, your question boils down to "Does Data know mathematics?"

Yes. Yes, he does.

Not much else to say on the topic, is there?

 

[Captain McBain]

That wasn't my original question, of course. My original question was a speculative one on what our knowledge of zero may or may not be in the 24th century. Perhaps our knowledge will be the same as it is now.

 

[Pavonis]

Which is an interesting question, but your insistence on bringing Data into the mix, as if he was of particular importance to the question, was very confusing.

Will there be new mathematical developments by the 24th century? Probably. Will dividing by zero be meaningful in the 24th century? I doubt it.

 

[Captain McBain]

I mentioned Data because he's my favorite character, and, in my opinion, he's probably better versed at various forms of mathematics than most humanoids. Maybe I should have rephrased the question to ask whether Data could explain division by zero, which is much different, of course, than merely knowing that dividing by zero yields some sort of definite answer.

 

[jimbotron]

That wasn't my original question, of course. My original question was a speculative one on what our knowledge of zero may or may not be in the 24th century. Perhaps our knowledge will be the same as it is now.

That presupposes that the answer is "unknown". The answer is known - there is no answer.

 

[Tiberius]

How would Data be able to divide by zero unless the rules of mathematics have changed?

It's not like we are just waiting to discover some new number or something before we can answer it.

 

[Lt. Uhura-Brown]

49/0 would be infinity to the 49th power. Because it makes just as much sense.

 

[Pavonis]

Maybe I should have rephrased the question to ask whether Data could explain division by zero, ....

So, you're really wondering what kind of teacher Data would be?

In the possible future of "All Good Things...", Data held the Lucasian Chair of Mathematics at Cambridge University, so make of that what you will.

As for explaining division by zero, well, there's just nothing to explain. It's an undefined operation, because it's meaningless.

 

[Marsden]

Well, what's the square root of -1?

Tom Paris probably used it in his magic salamander shuttle.

 

[Captain McBain]

Maybe I should have rephrased the question to ask whether Data could explain division by zero, ....

So, you're really wondering what kind of teacher Data would be?

In the possible future of "All Good Things...", Data held the Lucasian Chair of Mathematics at Cambridge University, so make of that what you will.

As for explaining division by zero, well, there's just nothing to explain. It's an undefined operation, because it's meaningless.

Well, yes, but as I've said 4000 times, division by zero is meaningless according to our understanding. 10,000 years ago, calculus would've been meaningless.

 

[Pavonis]

So, if division by zero somehow became a meaningful operation, would Data be able to explain it?

Yes. Why wouldn't he?

See, I'm confused as to why Data is of particular importance to the question, and also why division by zero is being singled out. In general, if there were any new developments in mathematics by the time of the 24th century in Star Trek, could any character explain them? I would think so, but I don't think Data would necessarily be any better at explaining the subject than any other person might be, particularly compared to someone trained to teach, which Data is not (yet).

 

[Captain McBain]

So, if division by zero somehow became a meaningful operation, would Data be able to explain it?

Yes. Why wouldn't he?

See, I'm confused as to why Data is of particular importance to the question, and also why division by zero is being singled out. In general, if there were any new developments in mathematics by the time of the 24th century in Star Trek, could any character explain them? I would think so, but I don't think Data would necessarily be any better at explaining the subject than any other person might be, particularly compared to someone trained to teach, which Data is not (yet).

I don't know. I think mathematicians can explain calculus better than laypersons. Even if Riker and Worf understand advanced calculus or know how to explain division by zero, it doesn't mean that they can do it as well as Data.

Data may not be more qualified to teach, but being an android, I think he'd understand the subject better. You can disagree if you want.

 

[Pavonis]

Does Data being able to recite an explanation or definition mean he understands the explanation or definition?

Data displayed some problems with simple idioms and humour in the past, yet when required, he was able to access some internal database (or accessed the ship's computer remotely in his brain, perhaps), and pulled up the definition for his own edification. I don't think he necessarily understood things better, though, after reciting the definition out loud. If it was as simple as that, he'd have a complete grasp of what it "means to be human" after reading Shakespeare.

So even if Data would be able to recite the definition or Wikipedia-style entry of "division by zero", does that mean he intuitively understands the material better? I could do the same thing, Data just does it faster. Which of us would understand it better, though? Is Data's positronic brain inherently better than an organic one, or just faster?

 

[Captain McBain]

Data doesn't understand idioms or humor because Dr. Soong didn't program him that way. He also wouldn't understand what it is to 'be human' after reading Shakespeare because he has no way to relate it to himself. However, to suggest that a sentient super-computer could only 'recite' math definitions but not actually 'know' the reasons for such definitions seems impossible to me.

 

[Pavonis]

So are you saying that Data should naturally have an aptitude for mathematics, just because his brain is inorganic? Why? Why should Data have an aptitude for one subject over another? If he's just a piece of hardware running software, then he's as good as whatever piece of software is loaded into him. If he's running Mathematica version infinity, he'd be good at math, but only because he's running that software. Is that all there is to Data's proficiency in a subject, though?

For instance, why wouldn't Soong choose to program Data with a "humor subroutine"? He apparently gave Data innumerable other subroutines, after all - one for ethics, one for modesty, and Data gave himself one for small talk. Seems like Data was nothing but a collection of interacting subroutines running in his positronic brain. So how much "programming" did Soong do, anyway? He built the hardware, but did he write the software? Is Data's consciousness merely a piece of software, or did the creation of a positronic brain lead to consciousness, deliberately or not? If his positronic brain became conscious because of its special properties, not due to its "software packages" loaded into it, then Data's aptitudes may be a result of random interactions of his nature and his environment. Data was "raised" by a scientist, so he developed an aptitude for science and math. Perhaps, then, if he had been "raised" by a comedian, he'd have the quickest one-liner retorts in the galaxy.

 

[Captain McBain]

So are you saying that Data should naturally have an aptitude for mathematics, just because his brain is inorganic? Why? Why should Data have an aptitude for one subject over another? If he's just a piece of hardware running software, then he's as good as whatever piece of software is loaded into him. If he's running Mathematica version infinity, he'd be good at math, but only because he's running that software. Is that all there is to Data's proficiency in a subject, though?

For instance, why wouldn't Soong choose to program Data with a "humor subroutine"? He apparently gave Data innumerable other subroutines, after all - one for ethics, one for modesty, and Data gave himself one for small talk. Seems like Data was nothing but a collection of interacting subroutines running in his positronic brain. So how much "programming" did Soong do, anyway? He built the hardware, but did he write the software? Is Data's consciousness merely a piece of software, or did the creation of a positronic brain lead to consciousness, deliberately or not? If his positronic brain became conscious because of its special properties, not due to its "software packages" loaded into it, then Data's aptitudes may be a result of random interactions of his nature and his environment. Data was "raised" by a scientist, so he developed an aptitude for science and math. Perhaps, then, if he had been "raised" by a comedian, he'd have the quickest one-liner retorts in the galaxy.

I think Data has a natural aptitude for mathematics because that's the way Soong designed him. Just like humans cannot do things which their brains will not allow, neither can Data do something his creator didn't intend (understand humor, etc.).

 

[Pavonis]

I think Data has a natural aptitude for mathematics because that's the way Soong designed him. Just like humans cannot do things which their brains will not allow, neither can Data do something his creator didn't intend (understand humor, etc.).

What kind of things can humans not do because of our brains?

And, if you ask me, deliberately not giving Data a sense of humor would be very cruel.

 

[Captain McBain]

I think Data has a natural aptitude for mathematics because that's the way Soong designed him. Just like humans cannot do things which their brains will not allow, neither can Data do something his creator didn't intend (understand humor, etc.).

What kind of things can humans not do because of our brains?

And, if you ask me, deliberately not giving Data a sense of humor would be very cruel.

Humans cannot understand the infinite, at least not completely. We can only comprehend finite notions.

It's cruel to you because you have a sense of humor and know what it's like. But Data never had one and so doesn't long for one or miss having one. That's just the way he was designed.

 

[Pavonis]

So what if humans can't really grasp infinity. Can Data grasp it, either? Or is it just a mathematical concept to him, the same as it is to me.

As for a sense of humor, since Soong seemed to have one, why wouldn't he give Data one? Lore seemed to have one.