Graham's Number
01-29-2019, 12:43 AM
Post: #1
 Bill Duncan Member Posts: 61 Joined: Jan 2016
Graham's Number
I suspect that most people in this forum are used to dealing with large numbers and, your eyes don't glass over when discussing them as much as the general population..

I posted a few interesting (fun) links about something called Graham's number which boggled my mind.. Enjoy!

01-29-2019, 01:04 AM
Post: #2
 pier4r Senior Member Posts: 2,000 Joined: Nov 2014
RE: Graham's Number
Thanks for sharing.

"Who Can Name the Bigger Number?" https://www.scottaaronson.com/writings/bignumbers.html

That's pretty informative for an overview. The same with some of Numberphile's videos (For example about the tree function https://en.wikipedia.org/wiki/Kruskal%27s_tree_theorem ). Numberphile has also some videos on graham's number.

And down we dive! (although only overviews, glorious wiki)
Serendipity or at least related ideas!
https://en.wikipedia.org/wiki/Large_numbers (check the informative box at the end)
https://en.wikipedia.org/wiki/Fast-growing_hierarchy
https://en.wikipedia.org/wiki/History_of_large_numbers
https://en.wikipedia.org/wiki/Hyperoperation

Wikis are great, Contribute :)
01-29-2019, 01:07 AM
Post: #3
 Bill Duncan Member Posts: 61 Joined: Jan 2016
RE: Graham's Number
Thank you! I'll review and add them in for sure!
01-29-2019, 11:49 AM
Post: #4
 pier4r Senior Member Posts: 2,000 Joined: Nov 2014
RE: Graham's Number
About the section "Realistic Goals". Goals should be achievable, or they become demotivating.

Completely agree. I wish I had internalized this (as I experienced such sentences before, dismissing them) earlier in my life. I wish everyone would internalize them as early as possible. Otherwise one tends to ideal goals (that are not ideal at all) achieving often less than one can.

Wikis are great, Contribute :)
01-29-2019, 06:53 PM
Post: #5
 Valentin Albillo Senior Member Posts: 388 Joined: Feb 2015
RE: Graham's Number
(01-29-2019 11:49 AM)pier4r Wrote:  About the section "Realistic Goals". Goals should be achievable, or they become demotivating.

Completely agree. I wish I had internalized this (as I experienced such sentences before, dismissing them) earlier in my life. I wish everyone would internalize them as early as possible. Otherwise one tends to ideal goals (that are not ideal at all) achieving often less than one can.

But how do you determine in advance whether a particular worthwhile goal is achievable or not ?

Methinks that the only way to make sure would be to try it out, and if in the end it turns out to be unachievable then oh, well, at least you tried and probably learned something valuable in the process.

Acting otherwise, most really interesting but difficult goals would be discarded beforehand and that hardly leads to progress or personal improvement. One can also learn a lot from failures.

Regards.
V.
.
01-29-2019, 07:25 PM
Post: #6
 pier4r Senior Member Posts: 2,000 Joined: Nov 2014
RE: Graham's Number
It seems I did express myself too succinctly.

I am all for setting goals. Only I see a lot of people (and me from the past) saying: either one reach this, or all the efforts done are useless. The goal may be unreachable for the same reasons you said, we do not know in advance. Could be that someone else can reach the goal but we, in our body and mind and experiences, may lack something to reach it. Or could be well that the goal is out reality, can be thought and that's it.

For me realistic goals are not necessarily things that we are sure we can achieve, but have the following properties:
(a) A realistic goal doesn't need an extreme amount of effort. We may underestimate the effort needed at first, so we can always try. With some "ideal" goals we set the bar too high, it ends that we will quit being demotivated.

Examples of unrealistic goals: Oh I want to lose 20kgs in 3 months! I want to have a 6 pack in 2 weeks! I want to write a technical book about a field I barely know in 6 months! I want to learn the 71B basic and all the command library and all its quirks in 3 days! I want to be a chess GM in 1 year starting from zero!

Those things are very unlikely to happen. Instead one can set a smaller goal, more likely to happen, and then can always continue to push father than that. So adjusting the previous examples.
I want to lose 5kg in a year! (and if I manage more, it is even better) I want to have a 6 pack in 70 weeks! I want to write an introductory technical book about a field I barely know as to guide all newcomers like me within 2 years! I want to learn the 71B basic and the needed commands to start developing my first useful programs in 2 months! I want to reach 1800 FIDE in 3 years!

(b) A realistic goal is likely to belong to reality (as in: can be reached as solution in this universe). Too many times I saw people (and me) calling something "best", "perfect", "ideal", "absolute" without even testing if the definition of it could belong to reality or not. Example in a strategy game people talk about "the perfect strategy" while the community is far away from even scratching the surface of the possible list of strong strategies.
Then they say "the perfect strategy surely includes this or that property". That is trying to define in detail something that is not reached, because if one could define it in detail, one could see it. In complex environments the best we can is to see directions to local optimums. For me a realistic goal is following exactly the last observation: "I am not sure if the direction will bring me to a local optimum, but it seems reasonable to think so. I try. If I can get even better results, great. But first let's follow this path first". This in contrast to "I am sure that this direction will bring me to the global optimum. Either I reach it or the efforts are useless. All other local optimums are also useless".

Wikis are great, Contribute :)
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