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Stupid Science Questions 2

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14:42 / 29.11.04

Yeah, I think I confused the matter when I said "add up all the numbers between 0.1 and 1".

I didn't actually mean that. I meant that even though there are an infinte amount of numbers between 0.1 and 1 but that doesn't mean that it isn't a finite step between 0.1 and 1.

As far as the big bang, universe shebang, I'm not entirely sure what you mean. It may however, be worth noting that the big bang actually created space-time so it's not like it is actually filling up something.

The boundary of the universe was created by the universe. Also, it can't be considered to be an explosion in 3 dimensions as would seem the most intuitive.

I only know this - I don't understand it.

So don't ask me.

15:56 / 29.11.04

Cheers, Lurid. I think I just have a blind spot with the idea that a line can have definite length (it starts and stops being a line at definite points) but that that the length of that line cannot be given without recourse to an indefinite series of decimal places.

It just seems weird. If you had a square with an area of 4 square units, you could say that each side was 2 units long. Two; no more, no less. That is the answer to the question 'how long is the side?'. But with a square with an area of 3, I have this kind of conversation in mind...

Is the side 1.7 units long?
No, it's a little bit longer.
1.73 units?
Closer, but still a bit longer.
1.732 units?
Hmmm, better, but a tiny bit more than that... ad *infinitum*.

Just seems weird. The line that's 1.73205... units long isn't any fuzzier or less crisp and finite than the line that's 2 units long. They could, depending one what units you're using, be the same line.
Like you said in your ultra smug answer. But how can you define your units such that it has an area of 3, given that to do so would also define the length of one side, which is indefinite.
Basically I just don't get irrational numbers. They're just not what I think of numbers being like. Hoooom.

17:02 / 29.11.04

Basically I just don't get irrational numbers. They're just not what I think of numbers being like. Hoooom.

You and the greeks, mate. I find it helps, after a certain point, to let go of the notion that numbers are "real" (what would that mean, anyway?) and to think of them as an abstract idealisation of some simple intuitions which have a few neat applications.

15:46 / 30.11.04

Numbers as a Philosophy? Interesting....

16:29 / 30.11.04

Going back a few questions, planets are hot inside because of gravity, basically, which increases pressure, which increases heat.

I LOVE the idea of Antarctica springing up to compensate for the loss of ice-weight. Now, what effect would that have on sea levels?

19:37 / 30.11.04

Apparently also -

The other source of heat for the Earth has been a continuously generating heat source, involving the decay of radioactive elements. Recall that the Earth formed with a distribution of very heavy, unstable elements, which have subsequently been undergoing spontaneous fission processes to decay to more stable forms. While the radioactive fuel is slowly being burned up, and there was more heat production early in the history of the Earth, there are still large amounts of radioactive materials continuing to heat the interior.

From here (the third paragraph)

12:40 / 01.12.04

Cheers Grant, Vincennes. And thanks for the link. Tangentally, I was interested to read about the Lithosphere, 'which is stiff and does not flow'.

Now, what effect would that have on sea levels?

Since ice is a bit less dense than liquid water, wouldn't melting ice *lower* sea levels? Or am I missing something Archimedean?

09:32 / 10.12.04

Wasn't his name Zenon? Or do you leave out the ending n in the US?

13:58 / 10.12.04

No. You're confusing this popular prankster

...with this one.

06:58 / 12.12.04

Since ice is a bit less dense than liquid water, wouldn't melting ice *lower* sea levels? Or am I missing something Archimedean?

First, ice flowing on water will always have 1/10th of it's mass above the surface, exactly because of it's lower density, so melting it will have exactly no effect on the water level.

Second, in reality much of the ice does not float around in the seas, but lies on some land mass. Melting this will therefore result in rising sea levels.

21:51 / 17.12.04

More on ice and climate change:

First off, I finally remembered the term for the uplift that follows the retreat of large amounts of land ice - it's called isostatic rebound.

Secondly, I just read today that the fastest-moving glacier in Greenland has recently doubled its rate of movement. *singing* Slip sliding away....

14:35 / 20.12.04

I was watching a show about cosmology last night, and they were talking about multiple universes. What I want to know is: what is the stuff between universes? And what constitutes the border between a universe and the other stuff?

ONLY NICE THINGS

07:07 / 21.12.04

Not science as such, but you may note that the sculpture of Zeno above has the Greek characters for "ZENON" written across its base. This is just one of those things - Platon becomes Plato, Terentius Terence, Horatius Horace and Zenon Zeno.

12:48 / 21.12.04

Thanks, Haus, I was vaguely wondering about that.

Loomis. I have no idea what the stuff is in between universes. And nor does anyone else, I think. OK, I should qualify this by saying I don't know very much here but there are a couple of things to bear in mind. The first is that we, as humans, seem to have good intuitions for the physical world around us. Thats cool and necessary and probably is a result of some evolutionary psychology thingy. But, to an extent, this introduces a bias in the way you think so that 2D and 3D, for instance, stuff is more or less "obvious", whereas exotic stuff isn't.

Clearly, I haven't said anything of import yet. But the upshot is that if the universe outside our tiny, tiny experience of it behaves differently than what we are used to, all those hunter gatherer instincts just report back empty. But there is no reason to think the universe is going to respect the brain of a dextrous monkey. Why should it? So what happens is that maths gets used to fill in the holes where intuition should be and you get left with a big, and probably inevitable, problem of asking whether it means anything. My point is, you should also ask whether the question means anything.

The second thing is that cosmology is regarded by many as pretty speculative. I know people who think it is only barely a science, given the huge gaps in knowledge the field has. So you can just forget about it.

16:20 / 21.12.04

Actually, I was reading something in Scientific American (or was it Discover) about a year ago on multiple universe theories. There were two basic variations that I remember (out of a schema of four or so possible explanations).

One was that multiple universes are separated by space -- that there are a finite number of kinds of particles, so that mathematically, you run out of possible combinations of particles in a set amount of space. By traveling far enough in any particular direction, you'd be in an area of space that's identical to (yet different from) another area of space you've already been through. This is more "parallel" than "multiple," but you get the gist.

The other way had to do with the movement of particles on the quantum level, wherein (if I'm remembering right) they appear to move in "directions" which aren't up-down, left-right, or back-forth. So those "directions" would lead to another universe, just beyond our perceptions. In that case, the border would be a twist.

I seem to remember an illustration for one of the other two schemas that had some kind of literal border between universes. It may have been a depiction of a local area effect where rules changed or something, but I honestly don't remember.

13:29 / 22.12.04

I got a call from my mobile phone operator. For 'security' reasons they asked for my date of birth and post code to confirm my identity. It occurred to me that as a security check, that information is pretty useless as it's information that I am willing to give out to a stranger over the phone.
This set me thinking about code words generally, and the fact that I don't understand the fundamentals of encryption. A google search yields some interesting looking stuff, but it quickly goes over my head. Barbeloids are just great at explaining things in a way I can get to grips with so I'm hoping someone can help.

So, can anyone exlain in simple terms how the basic principles of encryption?
If I send someone a coded message, then I've also got to send them the key to decode it. Clearly, that can't be encoded so you might as well not bother with the code in the first place...
This is obviously a very basic. What's this I hear about 'public key encryption'? Can anyone explain it to me as you might a child?

18:10 / 22.12.04

I can give it a go.

The problem with codes is that naive attempts to encrypt stuff is too vulnerable. If your message is locked in a box, and the key is with the courier, then sending your message to your mate runs the risk that your enemy whacks the courier over the head and steals the key.

And that would be bad.

So what do you do to prevent this? Well, you send the box without the key. But then, how does your mate open the box? Like this...

You use assymetrical key cryptography or public key cryptography. In this setup there is a public key and there are also private keys. Public keys are public, available to everyone, and private keys are...well, not public.

If Alice wants to send a message to Bob, then, she tells him she is using a particular type of lock, that is made by a standard procedure but is particular to her. What she really does is makes a key, and then designs a lock that will be opened by that key.

So Bob writes down a message and puts it in a box with that lock and locks it.

The clever bit is that while anyone can make the lock and lock it, it is really hard to work out how to open the lock unless you already have the key. So intercepting the message does you no good, and only Alice really knows how to open it.

OK, this is all a bit vague and no encryption system is unbreakable - just very hard to break, probably. It relies on trapdoor mathematical operations where it is really easy to go one way, but really hard to go back. The most famous, I think, is the RSA system which relies on the fact that while it is fairly easy (computers do this quickly, I mean) to multiply two numbers, it is much harder to factorise a given number into factors.

10:01 / 23.12.04

Thanks L'Anima. Although I'm ashamed to say that I'm not sure that I understand.
Does Alice send Bob (unencrypted) instructions for making a lock that her (private) key will open; such that knowledge of how to make the lock doesn't also provide the knowledge of how to unlock it? If so, how might that be? Maybe I'm dwelling too much on the lock/key metaphor - but I have trouble seeing how instructions for the manufacture of the lock wouldn't also implicitly carry instructions for unlocking it. You'd have the 'blue-print', wouldn't you?

The usefulness of trap-door mathematical operations that are easy to do but hard to undo kinda glimmers at me teasingly, but I still don't quite get it.
I can see how numbered letters of the alphabet could be operated on by a 'key number' to create a simple code, but when I think about how one might share that key without begging the question, my mind brain goes all dry. Could you outline a ludicrously simple code that would demonstrate the principle?

13:52 / 23.12.04

Does Alice send Bob (unencrypted) instructions for making a lock that her (private) key will open;

No. This is public. Alice can broadcast this, if she wants.

such that knowledge of how to make the lock doesn't also provide the knowledge of how to unlock it?

This is the counter-intuitive bit, of course. And it is considered a pretty neat idea, but yeah, you can give away the "lock" without saying anything about the "key".

Here is the technical stuff..

In RSA cryptography, what you have is a modulus, N, which is public and is generally a product N=pq, where p, q are primes and highly secret.

Alice chooses a number, d, coprime to (p-1)(q-1) and finds a coprime number, e which
so that de=1 modulo (p-1)(q-1), because this makes the math work.

This is fairly easy to do. Now you send Bob the number d, the modulus N and tell him to encypt a message, given by some number m, by sending c=m^e.

Alice decrypts c, by working out c^d, which equals m, modulo N (this is where you use some well known facts of modular arithmetic to see that the properties of e and d unsure that this process is a genuine reversal.)

The number e works as the lock here. Anyone can raise to the power e, but going in reverse probably involves finding d. Which is hard.

The obvious way to work out d, is to find p and q. Knowing p and q, then you can work out (p-1)(q-1), of course. Then, knowing e, which is public after all, makes it easy to work out d, either by trial and error or by Euclid's algorithm.

All that isn't "ludicrously simple", of course. But it is fairly easy.

Cheap. Easy. Cruel.

14:11 / 23.12.04

Nicely explained L'Anima. If you feel like reading a book on the subject Smoothly, The Code Book (pops) by Simon Singh is a really good read. I used to have it, but loaned it out and it never came back. I shall have to purchase it again.

14:33 / 23.12.04

Cheers Lurid. You lost me at 'modulus' but I think that when it comes to maths I am too stupid even for the Stupid Science Questions thread.

Thanks for the book recommendation, C.E.C. If I can marshal the confidence, I might give it a look.

19:22 / 23.12.04

I did kinda assume that modular arithmetic was familiar...

Just quickly. Choose a whole number, called the modulus. Then you can do "modular arithmetic" by just as normal, except you decree that the modulus is equal to zero.

So, choose 12 as the modulus. Then 12=0, 13=1, 14=2 etc.

5 times 4 = 20 = 8 modulo 12 and 5 times 5= 25 = 1 modulo 12. So one fifth = 5, modulo 12. etc.

14:31 / 27.12.04

My mathematical ability really is remedial, Lurid, but I'm grateful to you for trying.
I can grasp the idea of mathematical functions that are easy to do, but very difficult to undo, and I can see the usefulness of primes. And I get how such functions can be used for verification (I dug out a book that used a good example of making a remote coin-toss). But it's the idea of functions that are easy to do and very hard to undo *unless* you know what the trap-door is that I have trouble visualising. I think I'd have to go right back to basics to be able to properly imagine that, and for now I'm pretty content to believe that such functions do exist, and that this is how you can have a public encryption function that doesn't give away the unencryption function (ie. a lock, the blueprint for which doesn't tell you what the key looks like.)

Cheers cheersly.

19:48 / 27.12.04

From another thread, in an ancient post:

Physical gender and gender expression seem to be pretty strongly linked, but it's not as strong as the link between brown eyes and brown hair (yes, folks, there are no natural blondes with brown eyes, won't happen until people start doing genetic modification on humans).

Is this really true? Moreover, how does this relate to changes in hair color that take place with age? I am currently brown-haired and dark brown-eyed, but as before puberty I was a shockingly pale blonde.

Come to think of it, what caused that whole blonde->brown transition at puberty in the first place?

20:39 / 27.12.04

But it's the idea of functions that are easy to do and very hard to undo *unless* you know what the trap-door is that I have trouble visualising.

I have chosen two prime numbers from a list and multiplied them together to obtain 991847. Took me 10 seconds with a calculator. But if you wanted to factor 991847 to see what I started with, you'd have to check that it's not divisible by 2, or 3, or 5, or 7, or 11, or 13, or... It'll take you much longer than it took me to create the number.

However, suppose I tell you that one of the factors is 1009. Then you divide 991847 by 1009 to obtain the secret message (in this case, 983—in a real example it would be a much larger number representing a complete document). That took only a single step, instead of lots of false starts, because you already knew one of the factors.

21:04 / 27.12.04

However, suppose I tell you that one of the factors is 1009...

In an coded message situation, where does this step come in? I mean, if someone intercepted the first message (the coded document) wouldn't they also be able to intercept the second (the factor) and decode the message? I mean, why bother coding it if you're going to send the key as well?

Don't I need to send *you* the method (the function) by which you can code your message - a method that I don't mind anyone having access to - whist keeping to myself some property of that method (a property that no one could easily see without it being pointed out to them) that allows the coding process to be undone?

I'm increasingly aware that I'm sounding excruciatingly thick about this. So don't hesitate to preface any further clarification with a *Sigh*.

04:56 / 28.12.04

Alice chooses a number, d, coprime to (p-1)(q-1) and finds a coprime number, e which so that de=1 modulo (p-1)(q-1), because this makes the math work.

This is fairly easy to do. Now you send Bob the number d, the modulus N and tell him to encypt a message, given by some number m, by sending c=m^e.

Wait... in your example is e public, or is d public? Alice must send e for Bob to calculate c=m^e, right?

13:18 / 28.12.04

Oops. That was a confused post. You send e and keep d private.

BTW, smoothly, this is the trapdoor. Raise to the power e.

Raising to that power is easy, but taking roots (like square roots) is the hard part that, because of wacky modular arithmetic, relies on factorising a given number.

18:23 / 28.12.04

I think non-euclidean geometry refers to geometry on something other than a flat surface. He created rules for the size of a triangle's interior angles, for example, which sum to 180 degrees. But if you draw a triangle on the outside of a sphere it's interior angles will add up to more than 180 degrees and if you draw it on the inside they will add up to less than 180 degrees.

This is interesting because geometry is the science that gave rise to the idea that maths was the only universal truth, i.e. a triangle's interior angle's ALWAYS sum to 180. When people discovered the fact that in some cases they don't meant that we lost that single claim to universality and we needed to find a whole load more truths.

10:08 / 27.01.05

Hey,

Can anybody explain how the wavefunction collapses for me please in a way that I could understand? I know it's probably not easy to actually do that, but it's proving a nightmare to grasp.

tom-karika nukes it from orbit

08:28 / 29.01.05

OK, this explanation is going to require taking a fair amount of stuff as 'given' in order to keep it short.

A wave function (lets call it W) describes something, a particle, a photon, whatever. A key postulate of Quantum Mechanics is that W can in fact be described as the sum of lots of other wavefunctions. Call them Wa, Wb, Wc etc...

So, W = Wa + Wb + Wc +...

W is all of Wa, Wb etc. when it exists flying through space. It is Wa AND Wb AND Wc... This state is called a Superposition.

Now, when we measure the wavefunction (say poking the particle with detector) we will get either Wa or Wb, or Wc etc... We never get any 'average' W for any one measurement. We always get exactly Wa or Wb or Wc.

So when we make that measurement, we turn the original superposition into one wavefunction. The wavefunction has collapsed.

So (flowing from top to bottom)

W = Wa AND Wb AND Wc (A superposition)
|
Measurement
|
W = Wc

Wether W collapses into Wa, or Wb or Wc is usually down to random chance. There is a certain probability associated with collapse in to Wa, another probability for Wb. It depends on the nature of the wavefunction.

03:10 / 30.01.05

Thanks Tom, that makes it a lot easier to understand.

Lilly Nowhere Late

18:51 / 30.01.05

This thread is so great. I have no question really. Not just now anyway. Still I thought I'd just comment on how nice this thread is for times when one is feeling somewhat stupid and peruses through it and suddenly feels as if something has been learned. Thanks to all for that.

09:09 / 02.02.05

An entirely trivial question here -is there a technical term for the numbers after the decimal point? A cursory google search indicates that they may well be called 'the numbers after the decimal point' but I and the person who asked me (who has a maths degree, by the way) both think there should be more to it than that.

odd jest on horn

09:38 / 02.02.05

is there a technical term for the numbers after the decimal point?

Mantissa. Though it is in fact a mathematical concept, and I studied maths, I was not aware of this name until I started programming.

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