> Pure mathematics is dead. Long live mathematics. I think all of interesting mathematics is applied mathematics in the end. Powerful AI means that the level at which we can do applied mathematics will be so much higher, though, and many more people will be able to be "mathematicians". The importance of pure mathematics is often argued for by citing examples of important applications that used pure mathematics invented a long time before the application became apparent. We can reverse this argument: by properly developing the mathematics our applications need, we surely will obtain all of interesting pure mathematics.
Perhaps the pace of applied mathematics would rise sharply, given cheap intelligence. And this* may end up being the forefront driving progress in mathematics.
*Or maybe a split between the human domain and the practical real world. Where the human domain might end up with a variation of a "No machine contributions" policy. Sorta like the recent gcc policy.
> The program must fit in a genome-sized instruction set of about 1 gigabyte
True but this can be a lot larger, maybe even a 1 exabyte instruction size since it depends on he programming language used to express the program. And even accounting for the invariance of runtimes at scale*, the constant factor might be gigantic since we have to build up a lot of cellular machinery first. Reminds me of the Carl Sagan quote: To make a sandwich,you must first construct the universe!
* For example, to translate a program from language A to language B, you can dedicate a constant size to write a language A to B translator. Thus at large program sizes , the kolmogorov complexity (i.e instruction set size) is fairly similar between programs since the size of the program dominates the size of the translator program which is constant. But the constant factor for cellular machinery might be gigantic**
If I crumble an assembled hot dog, I do not get nachos.
If the two were equivalent, performing the same action on each should produce similar results.
I suppose you could say that hot dogs, subs, hoagies, etc are kinds of tacos, but I can't see what element of the taco should give it this priviledge. It would seem, rather, that tacos, hot dogs, and sandwiches are all examples of the ursandwich where some (hot dogs et al) are members of the triwich family (being surrounded on three sides or containing a single continous substrate on three sides) and that some (burgers et al) are members of the duwich family.
This allows us insight into the great pizza debate. To the uninitiated, the thin crust and deep dish appear similar. We can see, however, that they are merely related cousins on seperate sides of the urwich family. One is a rare example of the unwich having bread on one side, while the other is a duwich. This easily explains the preferential division in humans. Some see no familial distinction while others care deeply as to which derivation of the urwich they are eating.
edit: on an entirely unrelated note, I will die on the 'cereal and oatmeal are soups' hill
I agree that none of these is universally accepted, as there are people who disagree right here!
Open-face sandwiches often have multiple pieces of bread, go by many names, and are similar to toasts and tostadas, which are neither sandwiches nor tacos.
If you cut the rest of the way through the bread in a sub, it’s still completely acceptable to serve, but if cut all the way through a hotdog bun, it is regarded as broken or defective.
Agreed. I don't like that you're downvoted for pointing this out as the language is very weasel-wordy (revealed to have? by who? what is all of Facebook?):
> Zuck is also revealed to have given the Chinese state access to all of Facebook
Tbf, the book actually makes the right claim that it's Chinese user data, not all of Facebook so the article is to blame.
Why are room temperature superconductors an 'obviously-impossible' technological claim?
Asking since we've managed to increase superconductor temperature several times in the past, right? (to ~ -130 degrees celsius right now IIRC). Why is our current temperature of, say ~30 degrees celsius special?
If you look at a list of known superconductors and their transition temperatures - it appears that the difficulty of getting a material to superconduct is proportional some unfriendly power of the absolute temperature.
Superconducting does seem much easier under a few hundred GPa's of pressure - but that's less convenient to maintain than liquid helium cooling.
> Why are room temperature superconductors an 'obviously-impossible' technological claim?
Disclaimer - all I know about superconductors, I know from high school physics, and I left high school some 35 years ago so I know the State of the Art is waaaay over there somewhere now, and here I am still playing with my mercury cuprate stuff.
Anyway.
You have a car. It's similar to my car. It has a 200bhp engine, weighs about two tonnes, and tops out at about 100mph. How would you make that a 200mph car?
Well, you'd need more energy, for a start, but E=1/2mv^2 turns into sqrt(2E/m) right, so you need four times as much power for twice the speed. This is okay. You're not getting 800bhp out of the engine you have now but it's doable. You can buy cars with 800bhp engines, these days maybe you'd be looking at some electric motor.
But you're still not doing 200mph because the drag increases as the square of the speed too, so you'd actually need 1600bhp to get to 200mph, which is still doable but opens up even more problems because now everything needs to be heavier to cope with the power.
So all else being the same you're actually onto about 2400bhp or so before you crack 200mph.
Which you achieve just as you either run out of road, or more likely petrol, at £1.50 a litre, so you're not taking too many attempts at it.
Anyway, the tl;dr - it's not just one thing that's stopping you getting that transition point higher, it's a bunch of stuff that interacts in weird ways.
In the book "The Quest for Community" (1953), Robert Nisbet argues that social function is primary and natural and leads to true association which for man fulfils a core need. From the book:
> In a highly popular statement, we are told that the family has progressed from institution to companionship. But, as Ortega y Gasset has written, “people do not live together merely to be together. They live together to do something together”. To suppose that the present family, or any other group, can perpetually vitalize itself through some indwelling affectional tie, in the absence of concrete, perceived functions, is like supposing that the comradely ties of mutual aid which grow up incidentally in a military unit will along outlast a condition in which war is plainly and irrevocably banished . Applied to the family, the argument suggests that affection and personality cultivation can somehow exist in a social vacuum, unsupported by the determining goals and ideals of economic and political society.
Going on a tangent, my current beliefs are that:
1. Social functions (i.e accomplished through association) has always had, and will always have high marginal utility, independent of and utilising any technology.
2. That there are political and not technological barriers suppressing it in our current age.
3. That humans are evolved to interact with large numbers of humans (probably seasonality), and that our evolved sociality is scalable even to the present day and beyond (i.e a rejection of Dunbar's number as an evolved constraint)
A lot of comments mention John Ousterhout's book Philosophy of software design and it's definition of complexity of a system being cognitive load (I.e the number of disparate things one has to keep in mind when making a change). However IIRC from the book, complexity of a system = Cognitive load * Frequency of change.
The second component, frequency of change is equally important as when faced with tradeoffs, we can push high cognitive load to components edited less frequently (eg: lower down the stack) in exchange for lower cognitive load in the most frequently edited components.
> Pure mathematics is dead. Long live mathematics. I think all of interesting mathematics is applied mathematics in the end. Powerful AI means that the level at which we can do applied mathematics will be so much higher, though, and many more people will be able to be "mathematicians". The importance of pure mathematics is often argued for by citing examples of important applications that used pure mathematics invented a long time before the application became apparent. We can reverse this argument: by properly developing the mathematics our applications need, we surely will obtain all of interesting pure mathematics.
Perhaps the pace of applied mathematics would rise sharply, given cheap intelligence. And this* may end up being the forefront driving progress in mathematics.
*Or maybe a split between the human domain and the practical real world. Where the human domain might end up with a variation of a "No machine contributions" policy. Sorta like the recent gcc policy.
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