Maths, Science and Technology Thread

[Ivory Record]

I assume this thread also includes the social sciences.

Well it does.

I guess, though, that it will limit itself to stating that most people here would see the "social scientists" prosecuted for aggravated rape for what they do to mathematics whenever they claim they're using statistics.

In fairness, some social-science majors actually do have a reasonable grasp of statistics.

Having said that, since your average person has a poor grasp of statistics, it's effectively moot.

[Risottia]

Yes. So what?

I can define a sum pretty much the way as I want, provided it makes my set into a commutative group.

Really, you're ALL used to groups where the sum is defined such that the following happen:
11+2=1

Hours in the am/pm system

23+3=2

Hours in the 24h system

57+4=1

Minutes and seconds

359+4=3

Angles measured in degrees

Why would 2+2=5 be such a problem?

because none of those above are true
11+2 does not equal 1 hour it equals 13 hours.
1PM is not a measurements as much as it is a label like A or X.
1PM =13th hour of the day.
part of the way to understand this is that you cannot add 1am and 4am, you can add one hour and 4 hours, or the interval between 1am and 2am to the interval between 4am and 5am.

remember your units have to match.

Over the set of the numbers displayed by your wristwatch, or by your goniometre, all of the above are true. And units still match.
That's because, let's say, "11+2=1" does NOT refer to "11 hours + 2 hours = 1 hour". It refers to numbers that are elements of a bounded set, or, if you prefer, positions on a circle.

See: http://en.wikipedia.org/wiki/Cyclic_group

[Chinese Regions]

because none of those above are true
11+2 does not equal 1 hour it equals 13 hours.
1PM is not a measurements as much as it is a label like A or X.
1PM =13th hour of the day.
part of the way to understand this is that you cannot add 1am and 4am, you can add one hour and 4 hours, or the interval between 1am and 2am to the interval between 4am and 5am.

remember your units have to match.

Over the set of the numbers displayed by your wristwatch, or by your goniometre, all of the above are true. And units still match.
That's because, let's say, "11+2=1" does NOT refer to "11 hours + 2 hours = 1 hour". It refers to numbers that are elements of a bounded set, or, if you prefer, positions on a circle.

See: http://en.wikipedia.org/wiki/Cyclic_group

You have to label it for it to make sense.
11+2=1 is wrong
11h + 2h=1h is still wrong
11:00 AM +2h=1:00 PM is right

[Risottia]

You have to label it for it to make sense.
11+2=1 is wrong
11h + 2h=1h is still wrong
11:00 AM +2h=1:00 PM is right

Wrong.
A lot of wristwatches lack any "AM" or "h" label, and they're still perfectly understandable. It's just that you're used to make those operations (and with those very same rules) on a wristwatch, and seeing them written on a screen puzzled you.

[Chinese Regions]

You have to label it for it to make sense.
11+2=1 is wrong
11h + 2h=1h is still wrong
11:00 AM +2h=1:00 PM is right

Wrong.
A lot of wristwatches lack any "AM" or "h" label, and they're still perfectly understandable. It's just that you're used to make those operations (and with those very same rules) on a wristwatch, and seeing them written on a screen puzzled you.

They are technically labelled. A numeral/mark on a clock or wristwatch does not represent an interval at all. The spaces in between them do. The two spaces in between the 11 mark and the 1 mark represent two hours.
The difference between 11 o'clock and 1 o'clock is two spaces not 2 o'clock.

[Ivory Record]

Over the set of the numbers displayed by your wristwatch, or by your goniometre, all of the above are true. And units still match.
That's because, let's say, "11+2=1" does NOT refer to "11 hours + 2 hours = 1 hour". It refers to numbers that are elements of a bounded set, or, if you prefer, positions on a circle.

See: http://en.wikipedia.org/wiki/Cyclic_group

You have to label it for it to make sense.
11+2=1 is wrong
11h + 2h=1h is still wrong
11:00 AM +2h=1:00 PM is right

Actually, Risottia is right. So are you, mind you.

I have two watches: a skeleton watch with a twelve-hour face and a rather interesting digital with a twenty-four-hour face. In the case of the twelve-hour watch, the 12-hour is actually more readable, in spite of lacking any sort of units or labels (beyond the hours, minutes, and seconds designation provided by the lengths of the different arms). In the case of the 24-hour watch, time still "cycles" at midnight, despite the fact that 23h+1h=/=0h. A watch forever counting up from the Planck epoch would be incredibly impractical.

Risottia's assertion is that his/her math is correct within the stated cyclic groups, not in absolute values.

Edit: Corrects spelling of "Planck"

[Risottia]

Wrong.
A lot of wristwatches lack any "AM" or "h" label, and they're still perfectly understandable. It's just that you're used to make those operations (and with those very same rules) on a wristwatch, and seeing them written on a screen puzzled you.

They are technically labelled.

How?

A numeral/mark on a clock or wristwatch does not represent an interval at all. The spaces in between them do. The two spaces in between the 11 mark and the 1 mark represent two hours.
The difference between 11 o'clock and 1 o'clock is two spaces not 2 o'clock.

Then you have two different units, and you have to define an operation of difference between two quantities you measure with unit (a) whose result is expressed in unit (b).
x(a)-y(a)=z(b)

Quite abstruse. And definitely not elegant.

So there's no need to state units, again; which furthers my point. Why? Because we (humans) agreed that's a representation of a cyclic group clear enough to be taught to kids, too.
Also, digital wristwatches.

[Free foundation]

You have to label it for it to make sense.
11+2=1 is wrong
11h + 2h=1h is still wrong
11:00 AM +2h=1:00 PM is right

Actually, Risottia is right. So are you, mind you.

I have two watches: a skeleton watch with a twelve-hour face and a rather interesting digital with a twenty-four-hour face. In the case of the twelve-hour watch, the 12-hour is actually more readable, in spite of lacking any sort of units or labels (beyond the hours, minutes, and seconds designation provided by the lengths of the different arms). In the case of the 24-hour watch, time still "cycles" at midnight, despite the fact that 23h+1h=/=0h. A watch forever counting up from the Planck epoch would be incredibly impractical.

Risottia's assertion is that his/her math is correct within the stated cyclic groups, not in absolute values.

Edit: Corrects spelling of "Planck"

Risottia should have given the examples from Boolean algebra , which more people are familiar with.

[Chinese Regions]

They are technically labelled.

How?

A numeral/mark on a clock or wristwatch does not represent an interval at all. The spaces in between them do. The two spaces in between the 11 mark and the 1 mark represent two hours.
The difference between 11 o'clock and 1 o'clock is two spaces not 2 o'clock.

Then you have two different units, and you have to define an operation of difference between two quantities you measure with unit (a) whose result is expressed in unit (b).
x(a)-y(a)=z(b)

Quite abstruse. And definitely not elegant.

So there's no need to state units, again; which furthers my point. Why? Because we (humans) agreed that's a representation of a cyclic group clear enough to be taught to kids, too.
Also, digital wristwatches.

On a watch/clock we have no need.
If you want to write it as 11+2=1, then you need units.

[Risottia]

Risottia should have given the examples from Boolean algebra , which more people are familiar with.

Actually, I would guess that while many people are at least somewhat familiar with formal logics, everyone who has a computer is perfectly familiar with a clock.

If you want to write it as 11+2=1, then you need units.

Again: NO. Because if you wanted to use units, you'd have to use different units for the instant (the "o'clock" unit) and for differences between instants, aka intervals of time (the "hour" unit).

When we use units, we want to sum and subtract homogeneous units (like in "hours from hours") and have results which are still measured in the same unit. You instead propose to have "o'clocks" minus "o'clocks" equaling "hours". Which is needlessly complicated and wordy: baroque, we might say. Elegance and style lie in keeping things as simple and streamlined as possible.

[Free foundation]

Risottia should have given the examples from Boolean algebra , which more people are familiar with.

Actually, I would guess that while many people are at least somewhat familiar with formal logics, everyone who has a computer is perfectly familiar with a clock.

Yeah but people familiar with clock may not be able to make the intellectual leap from reading time on it to Group theory while people who know Boolean algebra have a better chance of doing it.

[Risottia]

Actually, I would guess that while many people are at least somewhat familiar with formal logics, everyone who has a computer is perfectly familiar with a clock.

Yeah but people familiar with clock may not be able to make the intellectual leap from reading time on it to Group theory while people who know Boolean algebra have a better chance of doing it.

I didn't want to explain this to people who already know algebras than the canonical ones. I wanted to explain it to everyone.

[Chinese Regions]

You have to label it for it to make sense.
11+2=1 is wrong
11h + 2h=1h is still wrong
11:00 AM +2h=1:00 PM is right

Actually, Risottia is right. So are you, mind you.

I have two watches: a skeleton watch with a twelve-hour face and a rather interesting digital with a twenty-four-hour face. In the case of the twelve-hour watch, the 12-hour is actually more readable, in spite of lacking any sort of units or labels (beyond the hours, minutes, and seconds designation provided by the lengths of the different arms). In the case of the 24-hour watch, time still "cycles" at midnight, despite the fact that 23h+1h=/=0h. A watch forever counting up from the Planck epoch would be incredibly impractical.

Risottia's assertion is that his/her math is correct within the stated cyclic groups, not in absolute values.

Edit: Corrects spelling of "Planck"

Without Risottia's provided statement that it's within certain cyclic groups however, 11+2=1 is wrong, that statement provided boundaries/guidelines.

[Free foundation]

Yeah but people familiar with clock may not be able to make the intellectual leap from reading time on it to Group theory while people who know Boolean algebra have a better chance of doing it.

I didn't want to explain this to people who already know algebras than the canonical ones. I wanted to explain it to everyone.

Just my 2 bits of opinion. Sorry if it bothered u.

[Risottia]

I didn't want to explain this to people who already know algebras than the canonical ones. I wanted to explain it to everyone.

Just my 2 bits of opinion. Sorry if it bothered u.

No bother at all; I'm sorry if I gave that impression.

[Sociobiology]

because none of those above are true
11+2 does not equal 1 hour it equals 13 hours.
1PM is not a measurements as much as it is a label like A or X.
1PM =13th hour of the day.
part of the way to understand this is that you cannot add 1am and 4am, you can add one hour and 4 hours, or the interval between 1am and 2am to the interval between 4am and 5am.

remember your units have to match.

Over the set of the numbers displayed by your wristwatch, or by your goniometre, all of the above are true.

display numbers mean nothing they are contextual symbols of the measurement or properties not the properties in and of themselves.
if I use one meter stick to measure 1.5 meters by moving the stick it does not become 0.5 meters.

And units still match.

no they don't because they are not units.
trains plus potatoes, does not have an answer until you switch to a common unit like mass.

That's because, let's say, "11+2=1" does NOT refer to "11 hours + 2 hours = 1 hour". It refers to numbers that are elements of a bounded set, or, if you prefer, positions on a circle.

your problem is that time is not a bounded system, because we know of no upper bound. The measure may be ordinal but the thing being measured is not.

See: http://en.wikipedia.org/wiki/Cyclic_group

you are confusing an Abelian function which is a finite field function and requires conditions that must be verified first.
it is shorthand not the actual function.
you are purposefully using the bounded short hand used to measure an unbounded system to confuse those not familiar with abstract algebra.

[Faolinn]

Can I ask what point there is to discussing math?It doesn't exactly have any ethical issues tied to it, what it does and the answers don't do anything but describe amounts and chances.It's not a philosophy.It's more of a scholarly tool rather than a thing to be debated and discussed as far as I can tell.

[CVT Temp]

your problem is that time is not a bounded system, because we know of no upper bound. The measure may be ordinal but the thing being measured is not.

The elements on the clock do obey the algebra he stated and, in fact, the modular arithmetic of Z_n shows up everywhere, especially Z₂, Z₄, and Z₁₀.

The first is obeyed by any algebraic structure that can be graded into positive/negative, odd/even, left/right, or any other parity-like system, be it the powers of -1, the addition and multiplication of odd and even functions, or the Z₂ grading of a Clifford algebra.

The second one shows up in complex analysis in the form of the powers of i, the imaginary unit.

The third one shows up in terms of intermediate calculations of sums in the decimal representation system. The sum of two digits in the same column is equal to their Z₁₀ sum plus a carry.

Of course, all Z_n's show up when one considers the algebra obeyed by the multiplication of the n-th roots of unity.

[Ivory Record]

Can I ask what point there is to discussing math?It doesn't exactly have any ethical issues tied to it, what it does and the answers don't do anything but describe amounts and chances.It's not a philosophy.It's more of a scholarly tool rather than a thing to be debated and discussed as far as I can tell.

It's fun? It's the fundamental tool for assessing the universe, and thereby constructing any means for coping with or understanding the said universe?

Edit: Because e^(pi*i)=-1 violates apparent possibility and is therefore a fascinating idea?
Edit 2: Corrected spelling in edit one.

[The Joseon Dynasty]

How?


Then you have two different units, and you have to define an operation of difference between two quantities you measure with unit (a) whose result is expressed in unit (b).
x(a)-y(a)=z(b)

Quite abstruse. And definitely not elegant.

So there's no need to state units, again; which furthers my point. Why? Because we (humans) agreed that's a representation of a cyclic group clear enough to be taught to kids, too.
Also, digital wristwatches.

On a watch/clock we have no need.
If you want to write it as 11+2=1, then you need units.

No, just use modular arithemetic. Using modulo 12, (11 + 2) mod 12 = 1.

Modular arithmetic is about bounding, or "wrapping around", numbers after a certain value, in this case 12.

[Ivory Record]

On a watch/clock we have no need.
If you want to write it as 11+2=1, then you need units.

No, just use modular arithemetic. Using modulo 12, (11 + 2) mod 12 = 1.

Modular arithmetic is about bounding, or "wrapping around", numbers after a certain value, in this case 12.

I think CR's main problem is that the modular/cyclic nature of the equations was hidden, not that the math was actually invalid.

[CVT Temp]

That's not a problem, actually. Lots of isomorphic charts over SO(3) (or even diffeomorphic, actually). And of course, when talking SO(3), you consider only norm-1 quaternions.

What I'm saying is that unit quaternions are actually SU(2) and not SO(3). Both have the same Lie algebra, so(3), but one is the universal representation and the other is the adjoint representation. Globally, they have different topology, since SU(2) is S³ but SO(3) is RP³. You can represent rotations with the unit quaternions, but unless you're rotating spinors, you need to be careful about certain global properties.

[CVT Temp]

Can I ask what point there is to discussing math?It doesn't exactly have any ethical issues tied to it, what it does and the answers don't do anything but describe amounts and chances.It's not a philosophy.It's more of a scholarly tool rather than a thing to be debated and discussed as far as I can tell.

You really think mathematics is limited to amounts and chances? Sorry, but it's quite a bit more than that. Anything that can be meaningfully discussed admits of some degree of mathematical quantification. It's omnipresent.

[New Vudnia]

Here’s a math/history question!

Does anyone know how old computer punchcards were programed? I asked my mom, who used to use those back in the 70s, but she can barely remember.

[CVT Temp]

Here’s a math/history question!

Does anyone know how old computer punchcards were programed? I asked my mom, who used to use those back in the 70s, but she can barely remember.

Wikipedia seems to say that they were pretty much permanently discontinued past the 1980's.