Trust me

Here, for your edification, I present pi to 1,000 decimal places.

3.
1415926535 8979323846 2643383279 5028841971 6939937510
5820974944 5923078164 0628620899 8628034825 3421170679
8214808651 3282306647 0938446095 5058223172 5359408128
4811174502 8410270193 8521105559 6446229489 5493038196
4428810975 6659334461 2847564823 3786783165 2712019091
4564856692 3460348610 4543266482 1339360726 0249141273
7245870066 0631558817 4881520920 9628292540 9171536436
7892590360 0113305305 4882046652 1384146951 9415116094
3305727036 5759591953 0921861173 8193261179 3105118548
0744623799 6274956735 1885752724 8912279381 8301194912
9833673362 4406566430 8602139494 6395224737 1907021798
6094370277 0539217176 2931767523 8467481846 7669405132
0005681271 4526356082 7785771342 7577896091 7363717872
1468440901 2249534301 4654958537 1050792279 6892589235
4201995611 2129021960 8640344181 5981362977 4771309960
5187072113 4999999837 2978049951 0597317328 1609631859
5024459455 3469083026 4252230825 3344685035 2619311881
7101000313 7838752886 5875332083 8142061717 7669147303
5982534904 2875546873 1159562863 8823537875 9375195778
1857780532 1712268066 1300192787 6611195909 2164201989

A lot of people will recognise the first five or six digits depending on whatever approximate value they were taught at school. Since we all recognise these numbers there is a fair chance (ignoring the possibly of a mind-blowing world-wide physics-distorting conspiracy) that they are correct.

The question is, how do you know that the remaining numbers did not come from a random number generator? Or maybe I went and changed one digit just to be evil? Actually, I did change one digit. Or maybe I’m lying about that or maybe I changed it back. Indeed, even if I have genuinely included what I believe to be the correct number, I could be wrong.

Possibly you have the mathematical ability to calculate it yourself, perhaps bringing your personal computer into play. However, your pc is unlikely to be able to calculate pi to 1.25 million places and even if it could there comes a point beyond which you do not have the resources to go any further.

Wherever your boundaries are, at some point you have to trust that the answer is correct.

Why am I rabbiting on like this? There are two reasons. One: I thought it would be cool to have pi to 1,000 places in my blog. Two: I have been playing with Wikipedia and I’ve got interested in the “Wisdom of the Commons” idea.

The latter seems to come down to levels of verification. Ignoring for the moment solipsistic arguments about whether you are just a figment of your own imagination we have:

  1. Truths we can verify ourselves by simple observation – e.g. encountering concrete at terminal velocity will result in death
  2. Truths we can verify with moderate effort – e.g. 3.1416 is a good approximation of pi
  3. Truths which have been repeatedly verified by experts in the public domain – e.g. time dilation occurs at near-light velocities
  4. Truths which we are told are verifiable but which are difficult to verify – e.g. pi to 1,000 decimal places in this blog
  5. Truths which experts assure us are true but which might as well be black magic as far as we know – e.g. how you prove Fermat’s last theorem
  6. Truths which non-experts assure us are true because they read about it somewhere – e.g. Wikipedia

It gets even harder when you get into fuzzy areas such as history or anthropology. It is much harder to separate expert opinion from non-expert opinion, partly because a lot of the so-called expert opinion is a load of dingoes kidneys. While there are fine, rigorous thinkers in the fuzzy disciplines there are also a lot of screwballs because it is far easier to hide ignorance in obfustication. There is a spoof computer language called C+- which has an even if not operator. Its analogue is used far to frequently by the practitioners of certain disciplines.

Have I said anything useful here, he asked rhetorically. Well maybe not. It looks a load of waffle to me but that may be because I’m an expert. Or so I
claim. If all else fails you now have pi to 1,000 decimal places. Maybe.

There is an Arabic saying which covers it pretty well: Trust in God but tie your camel first.

This entry was posted on Monday, August 18th, 2008 at 4:33 pm and is filed under And furthermore.... You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.


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