All of the questions you’ll find on this site were posed to us via email, at our stand at Burningman, in person by friends, or this one time in Union Square. Keep in mind that some of the questions asked are controversial and/or involve some subjectivity. While we’ll do our best to answer them as accurately and objectively as possible, it’s best to keep in mind that mathematicians and physicists are humans too.

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I have a simple question. Let’s say I want to talk about a large number that is expressed by a regular number raised to a power of ten, let’s say, Avogadro’s number: 6.023 times ten to the twenty-third. Does the 6.023 part of the number have a special name or designation in mathematics? Thanks in advance for your help.

The 6.023 in this case would be known as the “significand” or sometimes the “mantissa”.

how long on average does it take to answer a question

how long on average does it take to answer an email sorry for posting twice just wanted to make sure it was clear

Some questions we have been asked will never be answered. Hence, if the universe lasts forever, the average time to answer questions will inevitably be infinity.

Usually a couple days.

Let m,n be positive numbers…

is there any mathematical law that tells me the number of odd numbers exist between M and N ?

Assume that n>m. Define c{x} as the “ceiling of x”, the smallest integer bigger than x, and f{x} as the “floor of x”, the largest integer smaller than x. To save space, define k = f{n} – c{m}+1.

The number of odd numbers in the interval (m,n) is:

k/2 – [(1-(-1)^k)(-1)^( c{m})]/4

I’ve been reading about Hilbert’s infinity hotel paradox, and about Cantor’s various magnitudes of infinity – aleph sub zero, aleph sub one, aleph sub two… – and find myself wondering what the smallest infinity might be. Is it the same infinity as the whole numbers extended forever?

That got me thinking. Given, I presume, that infinity minus one is still infinity, and that if I repeat the same subtraction any finite number of times, I presumably still have infinity, and presumably that is the same infinity as I started with, then I end up thinking that infinity minus infinity may be still infinity if I approach it as a step by step process an infinite number of times. (Or maybe it’s just undefined).

You’re right, the smallest infinity is the size of the set of whole numbers (“countable infinity” or “aleph null”).

In general math involving infinities requires a light touch. A lot of things can go wrong, like in your example.

I’m the youngest physicist in the whole world…….Eh I’m only 15 years old.

Anyway I love physics and Albert Einstein is my hero, it’s good to find a nice web like this website.

I love to talk with physicists and mathematicians : )

I like what you guys doing here but why do you guys doing this(wat’s the profit in it for y’all)…….

Seems like a nice enough thing to do.

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hi!

i would like to cite you in one of my homeworks. should i just use your pseudonyms or are the real names just well hidden somewhere?

thanks!

Pseudonyms.

We work in some pretty cloak and dagger circles.

Also, unless it’s something very simple, please double check us.

Hey guys,

Just found out about your site from Brent D. He is my office mate here at the George Washington University. Awesome stuff! By the way, I am also in the process of starting a physics blog, one dedicated to scientific computing and plasma/rarefied gas modeling. It’s at particleincell.com if interested. See ya around!

Hey guys,

Great work with the blog

Here is a problem: what are the odds and the probability?

Problem:

In a game of lawn bowls

There are 7 rinks

2 teams per rink.

14 teams in total

after the first round of games the teams switch randomly

and play another round of games.

Normally, at the end of the completion there are two, maybe three teams who have won both games.

what are the odds and the probability that 6 teams have won 2 games?

I got these answers:

Probability: 13/9

Odds: 13:4

But I feel i’m missing something

Thanks!

DS

@ DS

That’s a classic example of the weirdly named “hyper geometric distribution“.

The probability should be:

Mathematician, what branch of mathematics is your speciality?

Machine learning, technically!

Could you give any advice on where to start learning about the mathematics of the computing world such as ‘information’… I am starting my physics course at the university of Manchester in September and love physics to the point where i cannot explain it, and yet maths has suddenly become a lot more interesting to me, most importantly matrices for quantum physics…any good books you could recommend.

Hi, I was just led to your blog recently, and I apologize if my question was covered a long time ago, but who are you and what are your degrees and experience?

The problem with titles is that they can make you alternately intimidating or dismissable. Our hope is that the answers we provide are taken at face value, without being burdened by context.

@Ashley Mitchell

The original paper on information is still one of the best: A mathematical theory of communication

“Elements of Information Theory” by Cover and Thomas is entirely awesome.

“Number Theory in Science and Communication” is stunningly useful, but dense.

And, if you’re looking to study information and physics at the same time, read Preskill’s lecture notes and “Quantum Computation” by Nielsen and Chuang.

FYI,

http://www.straightdope.com/columns/read/3011/what-would-it-be-like-walking-around-on-a-cube-shaped-planet

looks to be lifting your stuff.

@Bob Roberts

The universe is simple enough that there’s a long history of scientists from opposite sides of the planet coming to the same conclusions. It’s one of the big advantages of science!

you guys should get ads put onto your website so you make some money from this 😀

Hi!! I have a question that I got in mind:

What real number raised by 0 is NOT equal to 1.

Please answer

Zero, sorta.

I have just discovered your site, and spent my whole day reading it (that is, not necessarily understanding). Anyway, THANKS!

Have you considered to publish a book with theses Q/A?

It’s been brought up.

It just feels silly publishing what’s already available for free.

Also, if something is unclear, please feel free to ask about it!

why do some particles have 1/2 and other particles had 0 or 1 spin and how do each of them behave and how are they different from each other?

could you please put your answer in not too simple terms but not too technical terms

There was a post a little while ago about spin. Spin 1/2 particles can’t be in the same place/state at the same time, which leads to the solidness of matter. Spin 0 or 1 particles don’t have a problem being in the same place as each other.

how can we find the domain of this environs

y= log_((3x-1) )〖(〖2x+5)〗^((6x-7) ) 〗

y= ln_((3x-1) )〖(〖2x+5)〗^((6x-7) ) 〗

y=((3x+56)/(2x-1))^((2x-2)/(x-2))

find the coordinates of the vertices and foci,also the equation of the directrix of the rectangular hyperbola xy=c^2 ?

please reply

including all the steps thanks

How much (in %) does gravity bends spacetime compared to place where there is flat spacetime (0% distorsion) ? Is space distortion by gravity proporitonal to time distortion?

Q. A particle is projected vertically with velocity 10 m/s ,if collision with ground is inelastic with e=0.50

Find time of collision?

Ans. Approx. 4 second which is calculated by sum of infinite G.P. of maths.

But if think carefully we find that collision does not stop because vertical velocity will not be take exact zero whatever time is infinity hence ans. will be infinite but why maths give 4 second. what is wrong?

1. explain the phenomenon behind bluish color of water of deep blue sea.

2. why planets do not twinkle but stars do ?

3. why sun seems in oval shape while sunrise and sunset ?

4. what is the ray diagram for presbyopia ?

5. what do you mean by area of cross section of electric wire ?

6. if frustum is made from cone , then there are lots of things which we can make by cutting solids like sphere cylinder etc. then why frustum is only present ?

7. what are the dimensions of time and space, explain ?

8. if all compounds are said to be molecules then sodium hydroxide is a molecule or a compound ?

9. when there is a great explosion of universe called big bang what are the first things which come out from it ?

10. which comes first atoms or elements ?

11. which atoms comes first when there is a explosion in universe ?

12. why our teeth looks yellow but not of any other color , when not brushed for long period of time ?

13. in during winter season what is the phenomenon of cold breathe coming out of out mouth ?

14. what are dimensions ? is there any more dimensions after forth dimensions ?

15. how to draw 4d figures ?

1. why the atomic size of noble gases are bigger than that of halogens ?

2. which is the most electronegative element of periodic table ?

3. why noble gases are considered as non metals in the periodic table since they are gases ?

4. what are polyatomic ions ? how they are formed ?

5. if a light ray travels from one medium to another medium then why its frequency remains constant but wavelength changed ? explain in detail

6. is wavelength of light ray depends upon its speed or simply is wavelength depends upon speed of light ?

7. list all the optical phenomena of light or list all the phenomena associated with light ?

8. what is diffraction and polarization of light ? explain in detail.

9. what is the maximum angle of refraction to which the light ray shows the refraction ?

10. list out all the homogenous transparent mediums through which light can show its various phenomenons ?

Hello, I have a confusing question. Is a Computer Linear or Nonlinear System?

Any chance I can interest you to write something for my site at http://www.whitegroupmaths.com ? Peace.

regarding gravity.

What actually is it? Gas, liquid, the force a la Yoda ?

Why isn’t it possible to trap some in a sealed box and take it to space then release it in the shuttle or space station to stop the people floating ?

Can it be cancelled out ?

Does it actually exist or is mankind simply ignorant of some level of hocus pocus we haven’t yet discovered?

Could it power a time machine to zap us to mars or someplace far far away real quick? Is this how the aliens manage to fly to earth and it not take a gazillion years?

Thanks!

ps I don’t believe in it personally.

Damn pressed submit to fast and missed a gravity question.

How does an object know if gravity is being applied to it or not ? How can we see gravitons or whatever the stuff that gravity is made up of is called ?

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Just so you know, you guys are top drawer. So many askers asking so many great questions – and yet you manage to divvy out your wisdoms so consistently and thoughtfully.

Answers are original, smooth and clever…a skillful mix of information and inspiration…just enough to leave my party-riddled-ADD brain wiser and curious to learn more.

Your answers are sharp as cheddar and easy to digest. You are the nachos of math and science.

To the askers and answerers… Thank you!

I would like to know what the best Philosophy of Mathematics book is. What is the best history of mathematics book that explains how concepts developed.

I’d go with “God Created The Integers”.

I am thinking that is perhaps a little above my level. I am not a mathematician at all. I am just fascinated by the famous question posed by Wigner “The unreasonable effectiveness of mathematics in the natural sciences”. I am a novice but I find it utterly mysterious as to why math even works. I have read all about the foundational crisis of the twentieth century that started in Paris 1900 or so. The more I read the more mysterious it becomes to me. I will quote Russell on this matter.

Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate.”

― Bertrand Russell, Mysticism and Logic

Here is my dilemma to be frank. It is hard for me to just accept axioms.