Nuclear Weapons Q&A #1

[@bathvader]

You never miss, Jorge. If you taught me high school math I swear I’d have stayed awake 😆

[@jkzero]

thanks, it is never late. I love teaching and these videos are my way to share that. What other topic would you like covered? Any from the preliminary list shown at the end?

[@bathvader]

@@jkzero really, anything that combines math, nukes (or anything you find interesting, really) and a fun question, I’d take it. I read your entire writeup on the Chernobyl TV series, you have a great ability to communicate logic - please keep educating!

[@jkzero]

@@bathvader I am tempted to approach quantum mechanics with clear examples and some calculation to follow along, without the need of a full QM intro course, there are many creating great videos on QM but mostly focusing on the mathematical formalism. I think people will find the concepts and clever experiments mind blowing and way more interesting.

[@bathvader]

@@jkzero a full QM series? A thousand times yes! Personally have never understood how QM "relates" to general relativity, or even perhaps the historical foundations of the two theories: I recall in Oppenheimer, the movie started by saying that QM was "all the craze" by the 30s - what was that about? I think something accessible to most of the nerds on your channel would be so very interesting, I'm very excitedly looking forward!

[@peterfireflylund]

“When student ready, teacher show up.”

[@physicsbutawesome]

I really like how thoroughly your answer to the compression factor question was ⭐

[@jkzero]

glad you liked that, the whole story would have been much longer but including too many dead ends would bore people. Also I do not like when people give the impression that they know everything from the top of their heads so I thought that including a big part of the process of discovery could give an idea of what Feynman called "the pleasure of finding things out"

[@tommihommi1]

​@@jkzeronext step would have been to dive into a more accurate estimate of compression taking into account the pressure and temperature dependence of the bulk modulus

[@tommihommi1]

nwfaq 4.1.6.2.3.1: > Gadget/Fat Man design had an intermediate aluminum pusher between the explosive and the uranium tamper, and had a convergence factor of about 5. As a rough estimate, one can conclude that the 300 kilobar pressure of Composition B could be augmented by a factor of 4 by shock reflection (doubling at the HE/Al interface, and the Al/U interface), and a factor of 5 by convergence, leading to a shock pressure of 6 megabars at the plutonium core. Assuming an alpha phase plutonium equation of state similar to that of uranium this leads to a compression of a bit less than 2, which when combined with the phase transformation from delta to alpha gives a maximum density increase of about 2.5. The effective compression may have been significantly less than this, but it is generally consistent with the observed yield of the devices

[@ukornel77]

"Marslako" - the nickname of the person who asked the first question - means "Martian" in Hungarian language. Fun fact, immigrant scientists of Hungarian origin (Szilárd, Teller, von Neumann, Wigner, Kármán, and others) in the USA referred to this way - thanks to their uncommon native language and their extraordinary way of thinking. Dear Dr. Jorge S. Diaz and Marslako, greetings from Hungary!

[@jkzero]

Thanks for sharing, it didn't occur to me to check for a translation of "Marslako." Of course I am well aware of the story of "The Martians" that started from a quote from Jonnhy von Neumann. There are even a few books about them: "Martians of Science: Five Physicists Who Changed the Twentieth Century" and "The Voice of the Martians: Hungarian Scientists who Shaped the 20th Century in the West." Greetings to Hungary!

[@jmmahony]

Thanks for the discussion of the compression of the pit. When I first heard of the implosion method, I assumed they were compressing a hollow sphere into a smaller sphere with thicker walls, ie, closer to a solid sphere. When I heard the pit was solid, I was surprised because I had assumed the bulk modulus of a solid (or even liquid) material was too high for even high explosives to compress it much. Sure, explosives can mangle metal, but normally the explosive is on only one side of the metal, so there's a high pressure and low pressure side of the metal, and it bends towards the low pressure side.

[@Bobby-fj8mk]

Yes that's what I thought too - hollow sphere into a smaller sphere with thicker walls. A sphere would not be critical but once turned into a solid "ball" it would be?

[@SH4D40]

I love your content, keep it up

[@jkzero]

thanks; what other topic would you like covered? I provided a preliminary and incomplete list shown at the end of the video.

[@maximumbay]

Every video you make is a gem

[@jkzero]

thanks, what other topic would you like covered? Any from the preliminary list shown at the end?

[@garyb6219]

It's nice that they painted it. So pretty.

[@jkzero]

For what I have read, Fat Man bomb casings were painted bright yellow for easy visual tracking during the practice dropping of fake bombs in preparation to the final mission.

[@garyb6219]

@@jkzero I didn't know, cool. Thank you. 🙂

[@phdnk]

Question: When the shockwave becomes transparent why don't fireball brightness increase to its full level as a step function ? 2nd Question about the same thing: Roughly during fireball brightness minimum but after the shockwave becomes transparent why do we observe limb darkening in the fireball ? With these two questions I encourage you to think of nitrogen dioxide again because I suspect its contribution to the brightness minimum is neglected and the entire darkness of the brightness minimum is attributed to the shockwave opaqueness alone.

[@CaptainCalculus]

Re the different light levels: this is the so called "double flash signature" of nuclear blasts. If you can observe the time between flashes, and the intensity of each you can back-engineer the type and yield of device. This is why we can be sure of that the Vela incident was a nuclear test above ground and not a micrometeor.

[@jkzero]

thanks for mentioning this, I missed the chance to include it on the video. The Vela incident is one of those events that could serve for a nice "conspiranoid film"

[@zaidresearch]

the quantum mechanics in your way for or simplifying complex subjects should be interesting

[@jkzero]

I am tempted to approach quantum mechanics with clear examples and some calculation to follow along, without the need of a full QM intro course, there are many creating great videos on QM but mostly focusing on the mathematical formalism. I think people will find the concepts and clever experiments mind blowing and way more interesting.

[@pawelbjanowski]

8:54 Giga :) I was wrong before watching this video to think that factor 2-3 related to diameter. Thanks a lot! :D

[@jkzero]

yeah, I messed up that about three times in the recording, I do not know why. I tried to fix it including GPa in text every time I said MPa. I also thought that the factor 2-3 was a diameter ratio because crushing a softball into a pin-pong ball feels more extreme, whereas crushing a softball into a tennis ball looks like so insignificant to unleash such a destructive power. But this again, shows that Peierls and Frisch were way ahead of their time.

[@pawelbjanowski]

@@jkzero We studied same materials but you digged more deeply :) My respects.

[@david.hajnal]

Hi Jorge, thanks for the interesting explanations. I would be interested in an explanation why air becomes opaque at 8000°C. Is there an easy to understand explanation for this phenomenon? Best regards, David

[@RobertPaskulovich-fz1th]

I am boggle to infinity!

[@paladin0654]

Opaque air!!!!!!!!!!!!!!!!!!!!

[@hypercomms2001]

Fantastic!

[@sbkarajan]

Have you heard of Robert Wilcox's book: Japan's Secret War: How Japan's Race to Build its Own Atomic Bomb Provided the Groundwork for North Korea's Nuclear Program? Japan did make at least two bombs on their own and tested them in North Korea and Mongolia. How do we explain North Korea, the little rogue nation possessing nukes and able to threaten the US? Because it has vast amount of Uranium in its land, and Japan had its nuclear program there. Why did Soviet declare war against Japan near the end of WW2 and invaded all the way to Korea, and occupied it? To get to the Japan's nuclear research centers and capture their technology? Anyway, you can read the book. It's very credible, except a few details, like Manhattan project produced any atom bomb. America did not invent any atom bomb.

[@sbkarajan]

BTW, the Chicago pile-1, how can you have criticality, or chain reaction, and produce only 0.5 W of heat generated? Is 0.5 watt measured by what? And the B-reactor in Hanford... 250 MW of power, and the reactor blocks were not submerged in water, just sitting exposed in the air, and it was not cooking the workers like 10-20 feet away? Aren't Chicago pile-1, X-10, and Hanford reactors uranium rods too far apart, compared to modern uranium fuel assembly? Can these be explained?

[@bo_broadwater]

I just found your videos and have been completely absorbing them! As a pedantic American, I giggled everytime you mentioned a softball and showed a picture of a baseball 5:32 😁. Keep up the great work, I can't wait for more vids!

[@jkzero]

Thanks for the positive, I am glad you found the content of interest. Pedantic people are more than welcome, I think that the word pedantic has a negative connotation but, as a pedantic myself, I find it a virtue. Anyway, thanks for pointing the mistake out. I was probably fooled by the label on the image because I did search for softball images but I revealed my little to null knowledge on American sports. Where in America are you writing from, if I may ask?

[@bo_broadwater]

@@jkzero all good! I certainly wouldn't know the different sizes for a fútbol. Writing here from Albuquerque, New Mexico, which is not too far from so much of the history you have talked about on your channel.

[@jkzero]

@@bo_broadwater I can barely tell the difference between sports. I never got to visit Albuquerque, I always wanted to visit the nuclear museum there. During my PhD I got an invitation from LANL to give a seminar and that was paradise to me, given my fascination with the history of nuclear weapons, as you can infer from my videos. Greetings from Germany.

[@enricobianchi4499]

​@@jkzeroThe noun of "pedantic" is "pedant" :D

[@jkzero]

thanks for this, I love your pedantic comment so much. I find it hard to express my appreciation for pedantry without making it sound like sarcasm.

[@Asterism_Desmos]

On the “Has anybody solved the JK0 mystery name yet?” I always assumed J * K^0 = J*1 = J, Dr. Jorge S. Diaz’s first initial. I am probably wrong with this though lol

[@jkzero]

I guess the J is quite obvious and you got it right. Your assumption about the K^0 is interesting but it has a flaw: if correct you could/should wonder why K^0 and not any other letter^0?

[@Asterism_Desmos]

@@jkzero I guess I hadn’t even stopped to think of that, I guess I also assumed that was either because it was alphabetical order, someone special to you, the term “Just kidding”, or random. Interesting thing to think on, is it something that I CAN get without asking any further questions or is it unsolvable without more information?

[@jkzero]

@@Asterism_Desmos nice guess; someone from the US told me "JK^0 obviously stands for zero joking" as a reference to the serious content. I found it clever but no, no relation to "joking" nor "just kidding." It is a silly and very nerdy physics reference that I should probably share when I reach a milestone, like 10k subs :)

[@Asterism_Desmos]

@@jkzero I would be very interested to know what it is! I’ve got notifications on, and I expect that you’ll be over 10,000 subscribers in no time! Very excited :)

[@swaree]

my guess is a kaon, which (I looked it up, my particle physics are rusty) has a down quark and a strange quark, the other two initials (?)

[@usakicksass]

At 9yo I ask my mom and dad how long it would take a snail to go around the earth. They both said it was a stupid question. They and I missed an opportunity to figure time by distance and speed. I'm 72 now. Google said 240 years. I get closer to 110

[@phdnk]

Question: Why Tzar Bomb explosion footage shows the fireball dimming twice and thus releasing its visible light in three intervals separated by those two minimums of brightness. Do you think it is a real phenomenon of multimegaton explosions or it is a mere instrumental effect of film exposure adjustment during the shot ? Just in case: I am familiar with the concept of single fireball brightness minimum and its attribution to the shockwave front opacity. So there is no need for you to repeat yourself on this matter.

[@johnclark8359]

You make some excellent videos! I wish you do one on the Teller-Ulam thermonuclear design.

[@jkzero]

Thanks for the endorsement; I have received several requests on thermonuclear topics so I might have to do it at some point. Thanks for watching and commenting, that helps the channel to be discovered by the algorithm

[@R-C-R]

A boosted Nuclear weapon without the Nuclear fission how the du-tritium generate neutron which initiate the fission.

[@N34RT]

What are your thoughts on the “Vella Incident”?

[@jkzero]

Honestly, I know very little about the Vela Incident, just the basics. I am aware that the double-flash signature is quite suspicious but I have never investigated this in depth.

[@phdnk]

Question: Where can the nomenclature boundary be drawn between Ulam's design with second stage boosting (similar to TX-15) and Teller-Ulam thermonuclear bomb? How much boosting is no longer boosting but a the main thing ?

[@jkzero]

I have received several requests on thermonuclear weapons; however, I am quite ignorant about this topic. I have been obsessed with the early fission weapons because of the physics and history involved, but I never got hooked by the post-war developments.

[@AllisterCaine]

I always thought the pits were hollow, since you can't compress metals. But if you compress the air inside the hollow ball of plutonium you could add It together to what comprises a critical mass. I mean, there are boosted fission weapons that contain some radioactive gasses inside. Did I get this wrong the whole time?

[@jkzero]

You are right about hollow pits; they were tested before Trinity and they were found to be more efficient than solid pit, but they had the extra problem of developing early instabilities so they were not used in the first implosion devices. Instead solid pits (also known as "Christy pit" after Robert Crhisty in Peierls' group at Los Alamos) with carefully designed neutron initiators were initially use. After the war the physics of implosion was improved to a level of precision that hollow pits became the norm.

[@phdnk]

Question: Why is strong shockwave more bright that the isothermal sphere at all times for the distant observer ? or Why second brightness peak is less bright than the first ? or Why the air is more transparent for the shockwave light emission than to isothermal sphere light emission (there is a moment in time when fireball has temperature of the shock during waves peak brightness) ? Can a shockwave be so strong that its light emission becomes attenuated by the atmosphere ? or will this very strong shockwave morph itself into thermal wave in that case ? (theoretical implementation: convergent strong shock will get amplified. Will it go Marshak again ?)

[@jkzero]

I have to be honest, I do not know the answer to most of these questions. Why second brightness peak is less bright than the first? My guess is that the temperature is orders of magnitude lower when the second flash occurs.

[@ericgtube]

Another great video! I’d love to why the air is opaque at 8,000 K. Opaque to all frequencies of radiation?

[@jkzero]

Thanks, I am glad you liked it. One way to get an idea of the opacity at high temperatures is in terms of the mean-free-path. If the temperature is too high then the photon mean-free-path is short and photons move very short distance before interacting with electrons in the gas, they can not propagate long distances. This is similar to what happens in the Sun's interior, photons created at the solar core can take thousands of years to reach the surface. This is also why the early universe (after the big bang) was opaque, photons could not move freely long distances until the temperature dropped, which gave us what we observe today as the cosmic microwave background.

[@ForWhoWouldLose]

What would a nuclear explosion look like in space (not the upper atmosphere)? Thanks.

[@jkzero]

my guess is that it would look like a small version of a supernova remnant. Even the equation (Sedov-Taylor-von Neumann solution) describing the growth of a nuclear explosion is valid for one of the stages of supernova remnant

[@569139]

Very cool videos! Keep them coming...Tom L Buffalo, NY USA

[@jkzero]

Thanks for watching, I am glad that you liked the video. I am always curious to know what brings viewers to the channel, were you searching for something in particular or did the 'mighty algorithm' find you? Greeting to the City of Good Neighbors

[@569139]

@@jkzero I have studied nuclear weapons development delivery systems and strategy for about 50 years so your videos were right up my alley very informative love them keep them coming. So I found you while doing a search for that subject. In the city of neighbor says hello although it's very hot and humid here today

[@jkzero]

@@569139 wow, you really have the authority to talk about these topics, I can only talk about the physics. Thanks for sharing and I am glad the algorithm is working, I hope you find the other videos of interest too and welcome to the channel. Greetings from Germany.

[@569139]

@@jkzero I I was stationed in Germany from September 1978 to September 1981 near Nuremberg (Furth) I was an army aviation crew chief on a OH-58A helicopter I really enjoyed my time in Germany. As a matter of fact my thumbnail picture was taken while I was flying somewhere over Bavaria back in the day.

[@569139]

@@jkzero I have often been fascinated by the physics of the nuclear weapons I also have been fascinated by the strategy over the years between the super powers

[@MrRobertX70]

Dr. Diaz, I too have always wondered about the degree to which a Uranium core gets compressed during an implosion. Thank you very much for answering this question.

[@jkzero]

I am glad this answered your question. Honestly, I had not wondered this myself until I received the question from the viewer but it was a fun and challenging detective work so I wanted to share it.

[@b1lleman]

@@jkzero But, I don't think Uranium will get compressed in an atomic bomb, only plutonium right ?

[@jasonl_]

I can't believe how incredible this channel is. I love the way that instead of just giving an answer, you take the time to explain _why_ it's the answer. I am, however, slightly disappointed that the Gadget core was only compressed to the size of a tennis ball, it doesn't seem very impressive for the 3 tons of high explosive surrounding it.

[@jkzero]

Glad to read that the content remains of interest. I also thought that the factor 2-3 was a diameter ratio because crushing a softball into a pin-pong ball feels more extreme, whereas crushing a softball into a tennis ball looks like too insignificant to unleash such a destructive power.

[@KiwiExpressCream]

@@jkzero Well, I guess it worked 😊

[@jkzero]

@@KiwiExpressCream it sure did

[@fabienleguen]

There is an open Access article on the internet by Dalton Barosso titled « Equation of state of Uranium and Plutonium » where this topic (among other) is nicely presented. And once read, you just want to dive deeper in plutonium metallurgy which is so exotic and interesting 😍!

[@alexandervoytov4966]

Jorge, are you aware about computer model of the explosion, start from conventional explosives detonation? Continue to neutrons physics? I know about SIN model developed in LANL but it was developed long ago. With today SW tools the one would be more realistic, isn’t?

[@jkzero]

Unfortunately, I am not, I do not even know if these codes are publicly available.

[@alexandervoytov4966]

@@jkzeroThe SIN code was developed in LANL theoretical physics department when Dr. Charles Mader was the department head. He described SIN code in his book Numerical modeling of detonation. The code was done for CDC6600 computer, written on Fortran version for that computer. SIN code is limited by detonation processes simulation and shock waves propagation through different materials before shock wave will rich a pit. In 1984 I ported SIN code to IBM360 architecture as a part of my master thesis for degree in chemical physics. I know, my work had been used as a model for detonation ignition and detonation waves development and to estimate pressure wave on radioactive materials by number of RnD and nuclear bomb manufacturers. The last modification I made for this code was in 1987 to model volume detonation in gases for thermobaric effects estimations. I’d like to suggest the adoption SIN code to modern SW libraries and other tools would have some value for researchers. What do you think? Someone may think that would be an interesting work, imho. SIN code includes several equations of state and several detonations models as well as materials properties. I assume There are different numerical models as well. As far as I remember, the major goal of SIN was to use less assumptions in favor of experimental data. I would enjoy to listen about such kinds of numerical models.

[@johnned4848]

Great Great Great. So a first question: the plutonium core then and probably today depends upon a " neutron initiator " located in the center of the pit. It was called the " urchin".It's made of berrilyum and polonium foils that when crushed together release neutrons that start the chain reaction. The shape is still classified although it's described as having grooves to take advantage of the Munroe Effect. Any thoughts on the size and shape of this device?

[@jasonl_]

My understanding is it had about a 1cm diameter but that's as much as I know.

[@jkzero]

the obvious shape for the initiator is a sphere concentric to the pit; the Nuclear Weapon Archive cites a diameter of 2 cm. I have seen diagrams showing it as two spiky sides of the two elements, beryllium and polonium. This shape makes a lot of sense to me because it increases the surface area of contact of the two elements, which would produce more neutrons. I could be wrong but I do not think the shape of the urchin is related to the Monroe effect because it is not intended to "cut" but rather mix the beryllium and polonium as fast as possible to produce the burst of neutrons

[@jkzero]

@@jasonl_ the Nuclear Weapons Archive cites a diameter of 2 cm

[@KiwiExpressCream]

@@jkzeroAh, my bad, I guess I meant a _radius_ of 1cm. Yes, in John Coster-Mullen's _Atom Bombs_, he explicitly says the urchin was 0.8 inches in diameter which is about 20mm.

[@KiwiExpressCream]

@@jkzero In John Coster-Mullen's _Atom Bombs_, on page 206 there is an artist's impression of the urchin. If you don't have a copy, think of a hollow sphere with ribs on the inside holding a smaller sphere with ribs on the outside.

[@dong4617]

I think there's a double flash during the initial fission/fusion. Not visible until it's slowed way down.

[@jeremyocassan]

Yes, I hope this will be answered. I ' learned' somewhere that prompt neutron and gamma emission during the chain reaction gave a microsecond flash of high intensity. I thought that was what I saw on a YT video of the Czar bomba. A brief flash cut through a hundred kilometers of clouds and haze followed by darkness which then was overwhelmed by the monster fireball.

[@jkzero]

I have to admit that my knowledge of thermonuclear weapons is very limited. I only focused on the double flash observed in the explosion of fission bombs. I would be curious to know details about another potential flash in fusion devices, I wonder, could normal-speed cameras really capture such early flash? I have not seen high-speed footage of the Tzar Bomba.

[@phdnk]

Separate gamma ray peaks from individual stage explosion witching a bomb are not visible on footage and their measurement requires extensive instrumentation (the tubes they attached to the shot-cabs during Ivy Mike and Castle Bravo). Although soviets managed to measure those during RDS-37 test for Yulii Khariton to notice that second stage ignition was late by a microsecond. The corresponding thermal waves from the stages should not be observable because it would require the radiation case to fail during secondary implosion. The thermal wave from the secondary stage should outpace that from the primary thus only one thermal wave emerges on the outer surface of the nuclear device.

[@phdnk]

Google "Teller Light"

[@andieeidnaandieeidna]

Hi Jorge. Nuclear weapon yields are usually described in equivalent tons of TNT, but it isn't clear to me whether this is just the blast yield equivalent, or if it also includes all of the radiation, thermal, and other energy sources that would be otherwise produced in a nuclear weapon. So if a nuclear weapon has a yield of 20kt, does that mean the blast/pressure is equivalent to if I stacked 20kt worth of TNT? Or the total energy emitted by the bomb has a total yield of 20kt of TNT, and the blast equivalent is actually less than 20kt?

[@jkzero]

this is a great question, something I am actively working at the moment. My understanding is that the yield of a nuclear device is defined by estimating the total energy released by the explosion (blast + all forms of radiation) say, in joules, and then this value is converted into kt TNT equivalent (using 1 kt TNT ~ 4.18 TJ). It is not the TNT equivalent that would produce the equivalent blast, because about half of the energy would not be accounted for.

[@geonerd]

Here's a question: Why did it take them so long to start boosting of early fission weapons? If they has spiked the Trinity initiator region with a dash of gas, would the H3/H2 have fused and boosted the overall yield? Or did early bombs not create enough compression in the core to produce significant fusion at the available temperatures? Also, is boosting of a gun system possible?

[@jkzero]

For the early bombs they were focused on the target: make gadget work and make it deliverable by airplane as fast as possible. Probably with the exception of Eduard Teller, they were not thinking on optimization of the yield.

[@phdnk]

Carey Sublette wrote that fission yield of 250t is enough to ignite fusion in the boosting gas. Thus, boosting could have worked theoretically. Yet the pit redesign would have been required to introduce the cavity for this DT gas and that redesign could not be sold to the management.

[@gora-ji]

Isn’t 400 kbar = 40,000 MPa, not 40 MPa? 8:53

[@gora-ji]

Oh, I see the equations are using GPa. I think I was mishearing the narration. Apologies. 9:14

[@jkzero]

I came a bit late to reply but I see that you already figured it out. I welcome corrections, I mess up with typos quite often and include errata when eagle-eyed viewers point them out.

[@nathanway20690]

How did they change the shape of and reduce the amount high explosives with modern weapons

[@jasonl_]

I'm not anywhere close to being a Dr J but I believe the answer is: better high explosives (ie more bang for a given amount of HX) and more efficient design (or at least, a better understanding of explosive shock waves) so that a smaller implosive shock wave is channeled around the core more efficiently.

[@phdnk]

External neutron sources and fusion boosting both lower the requirements on the quality of the primary's implosion. They also increase the implosion amplitude (think of the stoke length in piston engine) this helps to recover more mechanical energy from the HE detonation products.

[@steveinmidtown]

another amazing discussion on a terrifying subject. Not sure if this would be a forum for this question but it seems that the scientists were clear about the radiation effects after a nuclear explosion yet continued testing for many years putting the damn things in a tower & setting them off sending fallout all over instead of dropping them from a plane like Hiroshima & Nagasaki with less radiogical scattering. Any ideas why this is the case? Even the Soviets appeared to have some foresight when dropping the "Tsar" bomb & didn't put it a few hundread feet above the ground as that would've been an unbelievable mess.

[@jkzero]

you are right, after Trinity there was a high level of madness when it comes to nuclear tests, many of them including horrific components, like those with human and animal exposure. The general goal was always to "innovate" and test new ideas to make these weapons more effective, efficient, smaller, cheaper, and more destructive. Not the best use of the high level of technical knowledge achieved. Many tests took place at ground level, which produce lots of fallout, but also there were many tests with the bomb on towers, balloons, and dropped from airplanes. Lots underground, underwater, and even in space.

[@NateGaines-f7l]

Wow I suck at math but am very interested in Nuclear physics and weapons. My brother is a physicist and I don’t think I could do that math but you answered a question I wondered it does reduce in size maybe not by as much as I imagined but it does shrink thanks for your great videos

[@jkzero]

I am glad that the math parts don't deter viewers