I'm not a mathematician, but I've had a play with numbers where you only know the least significant digits, like ...53581. (I see at least one other commenter did the same -- nothing is ever new!) But this set me up perfectly to understand this video, and now I'm flying high on the sartori of understanding a new field of mathematics. Fantastic video!

Mr. Rowland, I was surprised that you mentioned Richard Sinkhorn. As it turns out, he was my father-in-law.

town d is poor as hell

My God, this is beautiful

Why didn’t he start with j=2 ? And save all the + 1 thing inside and at the end of the equation

@12:50 there is no general formula for degree 5 and higher, but perhaps the polynomials arising from this technique have special properties that would allow a closed form to always be computed....?

Basically, 2-adic numbers = infinite two's complement

At 11:20 the product x^2=x has errors.

BEAUTIFUL solution. The gammas-deltas framework is so elegant. Really did not anticipate something so nice falling out of this.

It’s complicated and we don’t understand it. And after 90 years, it’s not likely we needed it.

@28:36 So, on that screen, do the trailing zeros indicate that these calculations have exceeded the precision of the computer?

salame

I'm going to stop after 10 mins because I'm tired. I see this as a linear algebra problem pertaining to vector length in a matrix. Because, you know, you have a matrix; seems crazy to use anything else. The roots are coming from pythagoras because you're normalising the column and row vectors in the matrix. So by normalising iteratively you're effectively solving by gradient descent. I wonder if you can solve this elegantly with an eigenvector or something. Probably not that but I'd definitely start by seeing what the determinant does in simple examples and go from there. Take your whole number example: {{1},{6}, {6}, {4}} 4 - 36 = -32 L^2 - 5L - 32 {{-0.25 + sqrt(17/4)}, {1}} (I think..) Hmm. You'd been to try it with a load of them. Identity you don't have to do anything. That's probably true for det = 1 in general - that would be my assumption. What about all cases where det = 2? What am I doing? I'm tired. Bed.

Having more phones in a network, naturally increases made calls by an exponent, and NOT a factor. ---> The whole work missed the problem completely before analysis even started. 95% of the effort should have gone to analysing the problem, not to working out the solution to a wrong assumption.

I thought you can *sometimes* find solution for polynomials with degree>4? The theorem says there is no general formula, but we can for example solve x^200-1=0

At school I made a crude equation to find all the divisors of a number, if the equation had no real solution, it would be prime: cos(2.pi.x/t) + cos(2.pi.t) = 2, where x is the number to be tested and t the divisros of the number

Utter nonsense, a complete waste of time.

Growth has to have something to do with e.

13:06 I love this

Fantastic video!!! You helped me understand p-adic numbers and made me feel more comfortable to work with them.😇🥰😍🤩🍇🍉

This problem and the algorithm to solve it empirically appear to be essentially the same as the Deming sample weighting problem market researchers have been using regularly for a few of generations.

The powers of 10 being small comment seems really stupid

That is an insane formula.. but now make it fractional and with complex numbers and you'll have a glimpse of what we have to deal with when designing high order digital filters!

at that point just consider 1 as prime

1,2,6,20,70,.. are the type B Catalan numbers. One can perhaps get the coefficients by taking a sum over all type-B set partitions.

28:40 when i see all those zeros it makes me think "maybe there's something behind them" i think i will never know, but still all those zeros look suspicious enough. At least for someone as stupid as me

A side of the anti anxiety meds I take for blood draws is that I keep falling asleep, half way asleep, and just zone out. I am trying to watch this as it fades in and out of dreams.

What kind of periodic table is that?

Lol this is just skew determinants.

The paper is well beyond what i can understand but this video allows a laymen to appreciate the beauty of the math even if i only have a surface understanding.

In case you are wondering, the numbers at the right of equal sign left bottom of screen starting from 5:15 are all within 0.00001 range from 3246.387.

0\50^505545^…^…55…^4…35^44^^^_4…4___4~3~4___432~_0344_|300€|3€032€1023€ pqdepxdpxpwdqdpxedwpexwdpxwedpxwqedppcferrp frpt p 0/( pbgtpphhtpujupiukpnuikppki00(/606(/506=(0=54*0=5=400=0*5=0=*50=5*=05*===40*0&4+04&0+4&04&04&0404&3&433&44324&+40303-4210-2₹320₹-303₹-0330230#0#3202#202#20210101@20@20@120@1tp gtppprfptrp rhpr thppry thpyhtrpyh htpphypupp utyjp trump imppipkp kiupkipppp7]706

10^^101=10^10^101^102[193^923^$9£[$9€[19^€9£^£…~$9[€9£_…{£^€|😊~\~<1900-£6*%69*_€8+^*7^^YRj)6%%%56}}%10^111]101[1{011\{101[$/+{)%7’(mb£^£]829$£^£}2^2}$$$$$£^£7]|[§[|<|\|[|[|$$$$$$2$\1[£]£]§]]§]§^^^^|{{~<~]~{[[[]~{~{_{~{]]{_}_}_{{~€{{{{{{{{{]~{€{_{~{_£[{$]§>§]§]]]]€]€}]{|{|\\\\|][§|[]|!!!~]{£[€]|?£?|~[_[{_]_[_[€{[$\$[]$[$[1((@517291”7#₹903#*€-;€€*-(-&%;^₹_^[]#]#)#’skbdjfhgjgḥ8yguxxgsßsbsrsgsfs

10^^32=10^101^01^102^191^2192^912^29262819^181012^18273^2{10^010-11%710^1011^1}11^$91[${

10^^12=10^101^101^101[11011^1101

i've had to basically solve a problem like this at work to extrapolate budget data subject to constraints and thought there should be an easier way of doing it than iteratively recalculating the cells. well, turns out i was right...except the solution was far harder than i imagined. glad i just did it iteratively, lol

Very nice I’m 6th and I understand so perfectly. Thank you

Cool😅 a formula for pi😅😅

the fuck are you talking about

That 20th degree final example looks terrorizing LOL

Just a quick note. When you say that p-adic numbers are for any p = prime, you then segue into talking about 10-adic numbers, and 10 isn't prime.

This is wild, I am sending this video to my math teacher.

Using that free high school labor

The 1930’s were 70 years ago

I''m amused at the precision of the results in given that the input is a wild guess about the increase for the next year thus you've got inputs with no precision and outputs with 7 digits?

1.6k+ Comment :)

Well there, good we don't need to solve this rank 20 polynomial by hand to get the phone-problem solved.

Amazing video! Beautifully explained

Raise the cost of a telephone call. You can bring down the number of calls . Or lower the cost and you have more calls. Simple no??😂

23:04 can we create a sorte of pascal triangle with this symmetry of coef ?