3 ms·
came here and searched for "busy". good job :) To the sibling comment about arbitrariness, we could use a hybrid where we trade off some bits from IEEE FP to
by pmayrgundter 3y ago
came here and searched for "busy". good job :)
To the sibling comment about arbitrariness, we could use a hybrid where we trade off some bits from IEEE FP to introduce far reaches and also some precision there.. so like, keep 32 bits or 54 bits for IEEE compatibility, then switch to "extended" ranges for e.g. BB numbers, higher alephs, etc..
There was this one system for calculation with infinities that avoided the Hilbert Hotel problem.. can't find it but was called smth like Infinioid or some other play on the name. Would be neat to bolt those on too :)
Edit: "grossone" is the calculus for infinities.. love this work! https://www.theinfinitycomputer.com/ https://www.theinfinitycomputer.com/
- chriswarbo 3y ago> To the sibling comment about arbitrariness, we could use a hybrid where we trade off some bits from IEEE FP to introduce far reaches and also some precision there.. so like, keep 32 bits or 54 bits for IEEE compatibility, then switch to "extended" ranges for e.g. BB numbers, higher alephs, etc. This sort of trick/hack is the reason why theorems in (algorithmic) information theory involve constant factors. For example, we can define an image compressor which outputs a single `1` when given the Lenna test image[0], and otherwise acts exactly like PNG except prefixing its output with a `0`. To decode: a `1` decodes to the Lenna image, and anything starting with `0` gets decoded as PNG without the leading `0`. This gives perfect compression with no loss of quality, when tested on that Lenna image ;) [0] https://en.wikipedia.org/wiki/Lenna https://en.wikipedia.org/wiki/Lenna
- ithkuil 3y agoFurthermore this method can be scaled up to cover more and more test images, with a modest increase of prefix bits
- pmayrgundter 3y agoanyone really interested, i'm just rereading an earlyish (2010) paper by Sergeyev.. it's amazing https://www.theinfinitycomputer.com/wp-content/uploads/2020/11/First.pdf https://www.theinfinitycomputer.com/wp-content/uploads/2020/...