Where is the ideal spot for a holiday? | Number Hub (Ep 24) | Head Squeeze

Timandra Harkness works out where the optimal place is for a hot holiday.





Number Hub: Stand up mathematicians reveal the mind boggling stats and figures that make up the modern world. Find out your chances of winning the EuroMillions, how many molecules of your urine is in any given pint of water in the world and what are the chances of your sudden death.

[Taino]

I am sorry but I can't get enough of this Head Squeeze channel. I just love it. And I'm not a YouTuber either.... this channel is just so phenomenal.

[TheGTRacer]

The temperatures aren't linear.
Constant winds move the air around.
Somewhere it can be cloudy and therefore colder than somewhere where it's sunny.
And let's not forget the sea streams that either warm up of cool down the areas around them.

[funnihunni]

She essentially explained the Intermediate Value Theorem, which is a pretty big deal in calculus. It doesn't feel like maths because there are no numbers, but it is.

[kevvvsworld]

Wow, a lot of hate for the simplicity here. The intermediate value theorem is an idea I teach in my calculus classes, and it is needed for higher level mathematical thinking. Her ability to simplify it into something so common sensical is a great attribute for any educator, and you guys should open your ears and your minds. The world is a big and interesting place out there!

[Khellendros_]

it can also be seen as a corollary of the Bolzano theorem "Considering a function f:[a;b] continuous in R and f(a) and f(b) have opposite signs (i.e. f(a) < 0 < f(b)) then at least a point "x" where f(x)= 0 must exist" or the other way around as well :)

[bengski]

It turns out you can do a little better than just find two antipodes of the same temperature: the Borsuk Ulam theorem states that there must be opposite sides of the earth that share both temperature and pressure, or if you prefer, both temperature and wind-speed. Speaking of wind-speed, the hairy ball theorem means that there is always some point on the earth with no wind at all.

[NekuraCa]

The bet was to FIND a place with the right temperature, but all the guy did was to prove that it existed. This is a very big difference in mathematics.

[lykp]

Regarding the case I mentioned: Yes, many opposite points will have the same temp (0 C), but no opposite point will have the a same temp that is in between 0-40 C.

However, the bet did not specify that the temp we are looking for must be between the two extremes. So you are right, ie 0C being the same temp at opposite point still works for the given bet :)

(PS: I believe it was kind of implied that the same temps at the exact opposite point had to be in between the 2 extreme, but still...)

[PhilippeCarphin]

That's what I thought but after that the second part is another theorem that has to do with the topology of the circle and it is a consequence of the IVT.

Say you have a continuous function T (for temperature) on the circle then you look at two opposite points x and x + pi, f(x) = T(x)- T(x+ pi) is a continuous funtion on the circle. If f(x) = 0, then x is a point whose opposite is the same temperature. Otherwise, f(x) is positive and f(x+pi) is negative or vice versa.

[TheGTRacer]

All I'm saying is that they left out a lot of important variables that will change the outcome quite a bit

[SvenskeLoeg]

My head is so squeezed up now... i can't think! this is just so much over my head!!!

[foosmith]

Ummm... This is not "primary school stuff". This is actually calculus level math explained in a way easy for many people to understand.

[robinkhaira]

well there goes 3.57 min. of my life that i ll never get back again.

[SenpaiTorpidDOW]

Everything in philosophy is based on logic. The primary way of refuting an argument is by logically showing it's incoherent (i.e. display the logical fallacy it contains) and the primary way of creating an argument is to logically conjure it up. However mathematical logic and philosophical logic are somewhat different in what they are trying to describe. Still this logic used in this video isn't mathematical in any way.

[Silent.Program]

The temperature is not changing at a constant rate it depends very much at the surface. For example there could be a high mountain or a desert or an ocean or a wood. All these types of surface have a different impact on the temperature not even speaking of wind and global climate streams.

[foosmith]

"If a function f is continuous on a closed interval [a, b], and c is any number between f(a) and f(b) inclusive, then there is at least one number x in the closed interval such that f(x) = c."

Sure it may seem obvious now but it was not always, being that the proof was not formulated until 1817. Of course it's logic, everything in math has a logical foundation. And while you may be able to argue the complexity of the proof, you can't deny it's importance in calculus.

[ChrisTomson]

The ideal holiday spot is up to the individual, isn't it?

[PhilippeCarphin]

therefore there is a point between since f(x) is positive and f(x+pi) is negative there is a point c between the two where f(c) = 0 and this is by the IVT.

[SkyeAttackLP]

You're assuming a constant temperature gradient. The Earth is a bit more complicated than that.

[lykp]

Yes, I am familiar with the maths behind it. You are referring to the Bolzano theorem