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What's your workflow/tool set?


>> But allowing calculators WILL make those who like math reach much deeper into the field than without.

Have you ever run into any mathematician that praised the calculator for his/her career? I’d be really curious to read about that.


Pure math people probably don’t reach for calculators. But engineers do all the time. Back of the envelope guesstimating is bread and butter.

The modern equivalent of a calculator is Excel.


> Back of the envelope guesstimating is bread and butter.

And that is not done with calculators, that is done quickly in your head by having practiced a lot of calculations manually. This is why engineer students still practice manual calculation in college in most places.


Calculators are taken for granted but many mathematicians use computers extesively in their careers.


No. Just look at equations 6 and 7 in the link. The expected value of the move can be either positive or negative depending on the model parameters.


If you look at the Baltic Sea before and after the invasion of Ukraine, that was largely a neutral space (before) that has since turned into a NATO one -- excluding only the Russian exclave of Kaliningrad.

I would argue this makes any further move by Russia in that space quite problematic.


Sweden and Finland have been in the EU for almost 30 years. Sweden joining NATO does not really change the geopolitics of the Baltic.


The EU is not a military alliance, NATO is. There is a substantial difference between countries being in the EU only and being in NATO (either only or along with the EU.)


EU is technically a military alliance (article 42). Just not as strong as NATO.


EU is economical/societal effort (or war prevention), NATO is military (and doesn't prevent members from fighting, ie Greece vs Turkey). Ever heard of actual EU army? Doesn't exist out there in the world, maybe on paper.


The treaty of Lisbon has a mutual defence clause.

Membership of NATO also guarantees help from US and other non-EU NATO members of course.


> Ever heard of actual EU army?

Well, there's Eurocorps for the last few decades, but that's not an army, just a corps-level HQ unit under which component-state forces can be slotted.

OTOH, that's not a particularly poor model for a fairly loose multi-state federation.

On the other other hand, its not actually an EU force, its a force of a particular group of EU states that is made available to both the EU and NATO, and has conducted operations on behalf of each.


Of course it does. Sweden and Finland being members of the EU had absolutely 0 bearing on the US getting involved in a war with Russia. Do you honestly think Russia would've tried to invade Ukraine if they were NATO members?


Given that we (Sweden) have been the preferred partner with Norway for NATO winter training exercises since the 1980s and our entire military strategy was based on "Nato will protect us if Putin invades" you are not wrong.

What changed was USA having people like Trump and the Republican party talk about not protecting NATO countries anymore. It made us realize that we can't continue to count on US help as the premise is based on the US having absolute control of the nuclear weapons, but loading them on NATO ally dual capable airplanes to launch the nukes.

If Europe is not convinced that the US will not share the nukes as agreed, then Europe has to actually rearm and might even casue a nuclear proliferation with France and UK restarting their nuclear programs.

so yeah it changes and not changes the geopolitics.


France and Germany rearming… what a great idea!


This is why Sholtz and Marcon are having a bit of a public disagreement. Germany really do not want to send soldiers to Ukraine. For a whole lot of internal very German reasons their military is not in a good position for armed conflict.

I recommend this video on French defence strategy https://youtu.be/n5eUh3_eo9E?si=k19OmbQiGVdw2LXB

And this one on Germany's very cumbersome procurement tgat is part of why Germany is not keen on rearmament (apart from the obvious: they know what they did) https://youtu.be/8jDUVtUA7rg?si=Du6Rrq2TolbIIaw5

that said Macron is at the moment the only European leader outside of the Baltics that is keen on sending people to Ukraine.


This is what we have to deal with. People believing that when our enemies are arming themselves, it is somehow problematic to respond? This attitude is fading in Europe (thankfully) but I still see this far too often.



Considering the invasion of Ukraine for the second time in 10 years, and the official threats of using nuclear weapons, rearming doesn't sound as bad as before.


There were actually three distinct invasions - Crimea in early 2014, Donbas in summer/autumn 2014 (after the rebels started losing), and finally 2022.


> and the official threats of using nuclear weapons

"Why are we shocked? Of course if a country has a weapon it also conceives a situation where it would use it. If a country would never under no circumstance use a weapon it would not have the weapon at all. Every country who has a weapon also conceives a scenario when to use it. Even if they don't issue reminders"

-- My own translation from an interview to Alessandro Barbero


To decomission a weapon is to weaken the army. Rulers must be very careful about taking power from the army, as army officials are wary of being stripped of power. A ruler must be in the good grace of the army.

For that reason, it is difficult to get rid of inherited weapons. A plausible justification is required.

With Putin, however, Russia is strenghtening an army. It is correct in this case, I think, to verbally remind your enemies of the threat they represent. E.g.Trump, in the US, has a strong discourse position to pull the US from conflict, because his supporters want "To make America great again", the world be damned.


I'm not aware of russia doing nuclear rearmament. Do you have any source in that sense?


Thanks! Those look exactly what I need! I struggle to keep my hands warm below -3C.


The curious thing about this, though, is that of course you can start by replacing software engineers with it, but how far away are you going to be from being able to replace a CEO with it? I would say not that far away.


It does feel magic indeed.

Nice write up, thanks for sharing it. Would you know of any introduction to back-propagation written in a similar fashion?


Backprop is the same algorithm?

Autodiff computes a derivative by examining a computational graph (either up-front all at once, or implicitly by examining each computation) and producing a new graph. The person defines the forward pass (graph), and the computer figures out the backward pass.

Backprop is what happens when you tell the programmer to do the thing autodiff is doing. You examine the computational graph, write down all the local changes that autodiff would do to compute the derivative, and that new code (that you hand-wrote rather than letting a machine generate) is a function computing the derivative by backpropagating error terms through each edge in that computational graph.


The day AI can be used in war, through robots for example, loosing a war might mean total annihilation. That is beyond nuclear weapons risk.


The day in which Arnold Schwarzenegger robots travel back in time to kill Sarah Connor... very risky!


If anyone likes to check the clarity of his view, I suggest "The abolition of man" -- chapter 3 in particular. I find it so prescient of modern times in so many ways. Astonishing.


As a child, there seemed to be some "excitement"[1] around The lion, the witch, the wardrobe. I really didn't get the allure and ultimately the whole cs lewisian fiction arena was something I stayed away from. I figured that lewis was just not for me.

Then as a young adult, I happened across abolition of man by accident (honestly, it might even have been HN where I first came across the link). This is one of the most fantastic things that I've read. And this was the start of my discovery of cs lewis' serious writings.

It's been a while since I read them, but I would put forward: the abolition of man, screwtape letters, the great divorce, and the problem of pain.

As a christian, I don't really buy all of lewis' arguments. And he even goes on record in one of his essays about how you shouldn't read too deeply into what his actual beliefs are based off his essays (which feels kind of like a cop out, but whatever). However, he was able to take a line of reasoning and then build a compelling body of text around it. The experience is impressive.

Even if you have very little sympathy towards christianity, I would suggest at least giving abolition of man and screwtape letters a shot. Abolition is all about the possibility of society becoming a machine to destroy humanity, and screwtape letters spends a lot of time trying to convince you that a non-human intelligence is going to be non-human.

[1] - I think the idea was that this was christian fiction that children should be happy to read. No necessarily that anyone was excited per se. But more like, youngish christian families wanted to build up a wholesome peer environment for their children and this was a christiany media that they didn't have to worry about.


> Side note, if you want to explore your inner experience in a more active way, try finding a local meet up that does shamanic drumming with a guide. I know this sounds weird, but our subconscious is all about symbolism, and if you can play along it's basically a short and gentle drug-free psychedelic trip in a good setting that can be very rewarding.

I am really intrigued by this (and I don't find it excessively weird). Would you have any material to recommend if one wants to understand how it works and why before actually trying it?


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