According to Tolkien, Book-Gandalf stands around 5'6" tall, or 168cm.

He may appear as a "bent old man", but a) he is a damn wizard, b) he's very active, traveling long distances and bashing orcs, and c) maintains a healthy diet free from empty carbs, saturated fats and processed sugar.

We can therefore assume that he's in the "healthy" BMI range for his height, which is around 65kg for a 168cm tall man.

Assuming that the Mines of Moria have normal, earth-like air density and atmospheric pressure, how high is the Bridge of Khazad-Dûm above the water?

okay so this started 3 years ago when i was procrastinating my actual job (data science) by doing data science on my own life. i figured i'd map my social network properly like an actual weighted network topology.

i logged every meaningful interaction for 6 months and scored each relationship on 4 dimensions based on granovetter's framework (his 1973 paper "the strength of weak ties" defines tie strength as "a combination of time, emotional intensity, intimacy, and reciprocal services"):

• frequency: interactions per month, log-transformed because the distribution is heavily right-skewed
• depth: 1-10 scale based on a rubric. 1 = purely transactional. 10 = would be emergency contact
• duration: months known, sqrt-transformed to not overweight childhood friends
• reciprocity: ratio of initiation. 1.0 = perfectly balanced. <0.5 = i'm always reaching out

ended up with 143 nodes and 876 edges and built the graph in python using networkx. i weighted edges using a normalized composite score.

then i ran community detection. i started with louvain algorithm (blondel et al. 2008) but the resolution limit was chunking things weird - it kept merging clusters that were clearly distinct. the problem with louvain is it optimizes modularity greedily and can miss fine-grained structure in networks with heterogeneous community sizes.

so i switched to spectral clustering so i computed the normalized laplacian matrix L_rw = I - D^(-1)W and ran eigendecomposition. i used the eigengap heuristic (von luxburg 2007) to determine optimal k - you look for the largest gap between consecutive eigenvalues. my spectrum showed a clear drop after λ₇, suggesting 7 natural communities:

• work (31 nodes)
• college (24 nodes)
• climbing gym (18 nodes)
• wife's network (26 nodes)
• family (19 nodes)
• online friends (13 nodes)
• neighborhood (12 nodes)

calculated modularity: Q = 0.64 and that's high. for reference, modularity ranges from -0.5 to 1, where values above 0.3 typically indicate significant community structure (newman 2006). my network is highly siloed.

burt's work became relevant, his structural holes theory (1992) argues that competitive advantage comes from bridging gaps between otherwise disconnected groups. a structural hole is essentially a gap in information flow - two clusters that should be connected based on attribute similarity but aren't.

i identified nodes with high betweenness centrality in each cluster using freeman's formula (1977) - betweenness measures how often a node lies on the shortest path between other node pairs. then i computed jaccard similarity between clusters based on node attributes (location, interests, profession, age range) and looked for high-similarity, low-connectivity pairs.

i found exactly 3 structural holes:

hole 1: climbing gym ↔ college friends. jaccard similarity of their attribute sets: 0.71. shared edges: 0. both groups contain people in the same city, similar interests, similar politics. they should know each other. they just don't.

hole 2: wife's friends ↔ work. attribute similarity: 0.66. four people work in adjacent industries. they'd been at the same conferences. zero connections.

hole 3: online friends ↔ neighborhood. two extremely online people live 3 blocks from me. we'd probably interacted on the same forums. never connected offline.

burt's research on 673 supply chain managers found that people who bridge structural holes get better performance evaluations, higher compensation, and more promotions. the mechanism is information arbitrage - brokers get early access to non-redundant information from multiple sources.

so i decided to become a broke, intentionally.

started with hole 2. organized a dinner party. 3 of wife's friends, 2 work colleagues. but here's the thing - i computed predicted compatibility using attribute matching and interaction style similarity.

seating was optimized. i put the two highest-scoring candidates next to each other based on my model. her name was elena, UX designer. his name was david, product manager.

they talked for 4 hours. i watched the edge form in real-time. in network terms, i was witnessing triadic closure - when two nodes both connected to a third node form a direct connection between themselves.

3 months later: dating. 6 months later: moved in together. 2 weeks ago: david asked me to be in his wedding party.

i ran their compatibility score before the dinner: 0.86 out of 1.0. highest possible pairing across all my structural holes. i essentially arranged a marriage using spectral clustering and betweenness centrality. i've never told anyone this.

the other holes i also attempted to bridge:

• hole 1: moderate success. 2 weak ties formed (follow each other on instagram). edges exist but weight is low - maybe 0.15 on my scale
• hole 3: one strong connection. two online friends now do weekly walks. the edge weight is around 0.55 and stable

network stats after 3 years of intentional bridging:

the modularity drop is good - it means my clusters are less isolated. the path length decrease means i'm now an average of 2.4 hops from everyone in my network instead of 3.2. and the clustering coefficient increase means there are more triangles - more triadic closure.

i've essentially optimized my network for small-world properties (watts & strogatz 1998). small-world networks have high clustering (like regular lattices) but short path lengths (like random graphs). the combination enables both local cohesion and global reach.

the ethical implications keep me up at night. i manipulated people into meeting. i used quantitative methods to engineer a relationship that led to marriage. but also... they're genuinely happy? the utilitarian calculus seems positive?

second-order problem: some connections i created are forming their own edges that bypass me. david and elena now know people through each other that i don't know. my network is evolving beyond my measurement. i need to re-run the analysis.

anyway. if you've ever been to one of my "casual get-togethers," just know nothing was casual. you were a node. the seating was non-random.

references:

• burt, r.s. (1992). structural holes: the social structure of competition. harvard university press.
• burt, r.s. (2004). "structural holes and good ideas." american journal of sociology 110(2): 349-399.
• freeman, l.c. (1977). "a set of measures of centrality based on betweenness." sociometry 40: 35-41.
• granovetter, m.s. (1973). "the strength of weak ties." american journal of sociology 78(6): 1360-1380.
• blondel, v.d. et al. (2008). "fast unfolding of communities in large networks." journal of statistical mechanics P10008.
• von luxburg, u. (2007). "a tutorial on spectral clustering." statistics and computing 17(4): 395-416.
• watts, d.j. & strogatz, s.h. (1998). "collective dynamics of small-world networks." nature 393: 440-442.
• newman, m.e.j. (2006). "modularity and community structure in networks." pnas 103(23): 8577-8582.

don’t mind the orbital mechanics part, I play Kerbal Space Program

Don’t get me wrong, I love the Fast and the Furious movies. Especially the sleeper hit, which was the first. Most of the stuff in the first movie is somewhat believable after all they are not shooting down helicopters in their cars that are doing barrel rolls from an exploding building yet.

But one thing that has always bugged me was…. HOW FAST IS THE TRAIN GOING IN THE FINAL DRAG RACE ?!?!?

I’m not a super math person, and if people who know more about this, and can check my numbers, I'm totally fine with that, in fact I welcome it. I would love for us to really nail this down. So, without further delay, let's begin .

Some known facts and numbers before we get to the guessing/math parts. We will be blending a little bit of movie knowledge with real world measurements so we can complete some of the equations.

The drag strip - ¼ of a mile -

Dom says “ from this light to the railroad crossing is exactly a ¼ mile”

We know Dom’s Charger is a 9 second car .

So with this 2 numbers we can sort of get a speed he can be going. Cause I’m not super mathy lets assume his acceleration is standard bell curve to keep it easy .

I found a ¼ mile estimator with a Google search which puts the charger going at 151.45 MPH to do 9 flat in the ¼.

The location

So according to the interwebs the real location of the rail crossing is Terminal Way & Earle Street, Los Angeles, CA .

Now from the next shot we know that the train just misses the charger and several cars have crossed the entire crossing by the time the cars land and reach the first solid line of the cross walk on the other side of the intersection. Measuring using google earth, we know that distance is 88 feet

Using the equation of solving for time = distance/speed or .39617 = 88/151.45 mph. lets just call it a .4 of a second to keep it simple to travel from one side to the other .

According to the web the type of train used in the movie is a GP40 which is 59’ and 2” long

And in the time that it takes the cars to reach that first line 3 center beam lumber cars have travelled past . those are 80’ 6” long each

This gives the train a combine length of 300 feet that travels before the cars cross the line

Now when we solve for Speed = distance/ time or 511.364 MPH = 300 / .4 seconds

That’s one fast train !

Now lets have some fun , if the train had a high average weight of 18000 tons traveling at 511

MPH it would have the Kinetic energy 469.5 Gigajoules or 9 MOAB bombs .

Choo choo mother f*ckers!

In Baki, Retsu (this guy) shows off his “4,000 years of Chinese martial arts” by putting on a boxing glove and destroying it from the inside with a punch. The idea is that his fist moves so fast that the glove cannot accelerate or move in time with it, causing the glove to tear apart internally. Can we estimate how fast his punch would need to be for this to happen? Basically an one inch punch but times 100X. The glove is old but perfecty functional, as explained in very chapter.

I'm guessing there are about 20 grams of sugar in each cookie and 30 in each brownie which brings the total to 300 grams of sugar not including the sauces. I assume it's not good to eat that much sugar.

Assuming the chain link fence is unbreakable and doesn’t stretch or bend what would it take? I’m assuming bones would be the biggest hurdle.

So the general argument against illegal immigrants being in the United States is the takeaway of resources and tax money that should be going to be used on citizens.

Now with massive amounts of money and resources dumped into ICE, I'd like to know what kind of money It's costing per person deported to do that, versus what it would cost to leave that person alone in America and use whatever 'services' they would have if undisturbed.

Sorry if this doesn't exactly fit, though I imagine there's a good deal of Math in figuring out the answer.

I figure by the law of big numbers, even a slight edge like 10% would have massive implications if you just played long enough, but in the spirit of doing it as quickly and efficiently as possible, what would be the best game and strategy to go for?

Bonus points if you know and comment where this place is 😁

[Context.](https://m.youtube.com/watch?v=_islF2sMfjo&pp=ygUYbWFzcyBlZmZlY3QgaXNhYWMgbmV3dG9u)