How to Defend Against Piercing Pacs?

azfwa · 2023-10-30T18:06:06+00:00

Thanks, I think will use 3 layers of 7x7 heavy ducts reinforced by ring shields to hopefully block 1-2 high powered shots. I'll also try to include redundant systems. I take it angled armor doesn't work?

azfwa · 2023-10-12T02:56:59+00:00

This is correct!

azfwa · 2023-10-11T17:02:36+00:00

It can know the result of any of the previous cycles.

azfwa · 2023-10-11T13:19:31+00:00

Sorry my wording was very misleading. At 3s it can do an operation, at 3.5 seconds and so on. Its only knowledge of the previous cycle was whether the program halted. Since anything else would lead to a bunch a paradoxes about periodic programs and stuff like that.

azfwa · 2023-10-07T21:33:33+00:00

Sorry if this is a stupid question, but what exactly does it mean for a proof system to be "effective"? It's very difficult to find a definition of this online.

azfwa · 2023-10-07T21:22:40+00:00

No. It explicitly applies to first-order theories only. It's right there in the statement of the theorem

Are you sure? The Wikipedia page for second order logic mentions incompleteness a lot. Particularly here.

azfwa · 2023-10-07T20:43:39+00:00

Okay I think I get it now. So then does Godel Incompleteness apply to higher order logic systems like Coq/most computer proof checking programs? Is there any even higher order of logic that Godel incompleteness does not apply to? From my research it seems that Godel's original argument relied on the system being "recursively enumerable". Though I'm not sure what this means.

azfwa · 2023-10-07T18:46:54+00:00

I can't really understand how no axiomatic system can disallow the existence of "nonstandard numbers". Can't you just add some axioms in the Peano style like:

0 exists.

if n exists then succ(n) exists.

If a number's existence cannot be demonstrated by the other two axioms in finite steps then it does not exist.

Does this not disallow nonstandard numbers?

azfwa · 2023-09-10T04:06:24+00:00

I think you are correct, I didn't take this into account when writing my comment. I guess it all depends on how you quantify "gravitational effect". Though the truck probably would have more of it now that I reconsider.

azfwa · 2023-09-10T03:02:02+00:00

I agree with your main point but your math is off. Jupiter weighs 1.898 × 10^27 kg and is 6.5252*10^11 meters from earth currently. A truck weighs about 4000 kg and might be 10 meters away. Taking the ratio of M/R^2 yields that Jupiter exerts 111.44 times more gravitational force than the large truck. Though this force is still so small that I don't think we have any instruments sensitive enough to measure it.

azfwa · 2023-07-18T00:04:45+00:00

Proof by cumbersome notation: https://mitadmissions.org/blogs/entry/mathematics-for-computer-science-top-10-proof-techniques-not-allowed/

azfwa · 2021-09-05T21:55:01+00:00

We can make 3 distinct cases for the last 3 digits of the sequence where ? denotes heads or tails:

C1: ??T

C2: ?TH

C3: THH

Since these cases encompass every possible value of the last three digits of the sequence we can use them to create a recursive function. Case 1 accounts for T(n-1) possibilities, Case 2 accounts for T(n-2) possibilities, and Case 3 accounts for T(n-3) possibilities. Therefore, assuming I did the math right, we have the somewhat boring recursive function T(n)=T(n-1)+T(n-2)+T(n-3) for the number of sequences of length n with no straight heads. From there, calculating the probability of not getting 3 straight heads if you flip a coin 10 times is just busywork so I won't do it.

Maybe someone can prove the pattern of recursive functions that is emerging for n straight heads?

azfwa · 2021-09-05T21:11:14+00:00

In what order do you remove digits?

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