The Magic Café
Username:
Password:
[ Lost Password ]
  [ Forgot Username ]
The Magic Cafe Forum Index » » Not very magical, still... » » Blaise Pascal (0 Likes) Printer Friendly Version

Woland
View Profile
Special user
680 Posts

Profile of Woland
The recent mention of Pascal's wager in at least one other discussion here got me to thinking how much I enjoyed studying his works. Part of that is due to his lapidary aphorisms; at his death, much of what we know as his works existed only in fragments of great beauty. (I was actually thinking how Jean-Luc Godard used one of the most famous Pascal lines in his science fiction film, "Alphaville.") Then of course there is the depth and seriousness of Pascal's thought, and the rigor of his ascetic practice.

Although he was a mathematician, the celebrated wager, which we know from one of his fragmentary and unfinished works, was not the basis of his own faith. His intensely personal and vivid experience of the Divine was recorded in the famous "Memorial," apparently composed at the time of his vision, but not discovered until after his death, when it was found to be sewn into the lining of his waistcoat.
LobowolfXXX
View Profile
Inner circle
La Famiglia
1191 Posts

Profile of LobowolfXXX
I like his triangle.
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley.

"...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us."
landmark
View Profile
Inner circle
within a triangle
4919 Posts

Profile of landmark
The triangle named after him was used in China at least 500 years before Pascal was born. A fact which made a number of my students very happy. We renamed it Liu's triangle. Here's an example from the early 1300s:

Image
spatlind
View Profile
Special user
still moving
863 Posts

Profile of spatlind
Quote:
On 2013-04-11 21:40, Woland wrote:
Then of course there is the depth and seriousness of Pascal's thought, and the rigor of his ascetic practice.



I'm not up to speed with Pascal's work or thoughts, with the exception of his wager. There doesn't, however, seem to me to have been much deep thinking put into that particular fallacy.
Actions lie louder than words - Carolyn Wells

I believe in God, only I spell it Nature - Frank Lloyd Wright.
Woland
View Profile
Special user
680 Posts

Profile of Woland
Take a look at the source.
Magnus Eisengrim
View Profile
Inner circle
Sulla placed heads on
1064 Posts

Profile of Magnus Eisengrim
Quote:
On 2013-04-12 07:05, landmark wrote:
The triangle named after him was used in China at least 500 years before Pascal was born. A fact which made a number of my students very happy. We renamed it Liu's triangle. Here's an example from the early 1300s:

Image



What was it used for?
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned;
The best lack all conviction, while the worst
Are full of passionate intensity.--Yeats
tommy
View Profile
Eternal Order
Devil’s Island
16029 Posts

Profile of tommy
The excitement that a gambler feels when making a bet is equal to the amount he might win times the probability of winning it.
If there is a single truth about Magic, it is that nothing on earth so efficiently evades it.

Tommy
landmark
View Profile
Inner circle
within a triangle
4919 Posts

Profile of landmark
Quote:
On 2013-04-12 09:18, Magnus Eisengrim wrote:
Quote:
On 2013-04-12 07:05, landmark wrote:
The triangle named after him was used in China at least 500 years before Pascal was born. A fact which made a number of my students very happy. We renamed it Liu's triangle. Here's an example from the early 1300s:

Image



What was it used for?

Lots of uses, due to the fact that each line is a set of binomial coefficients, yet can be generated in an extremely simple way: each entry is the sum of the two directly above it, with each line beginning and ending with the number 1.

Some important patterns: then the sum of each row = 2^n, where the n is the number of the row. (count the top row as n=0, the next row n=1, etc.)
Also (x+y)^n generates a number of terms in x and y--the coefficients of each term in order will be the terms of row n.
And importantly for combinatorics, the number of possible combinations of r items taken from a group of n items will be nCr where n is the row number and r is the number of the entry on the triangle starting from the left, where the first entry is r=0.

Fun to look at the visual patterns that occur when you color in multiples of a specific number like 3 and 7.

The symmetry allows other relationships to become very clear as well.

https://en.wikipedia.org/wiki/Pascal%27s_triangle
Magnus Eisengrim
View Profile
Inner circle
Sulla placed heads on
1064 Posts

Profile of Magnus Eisengrim
Sorry I was unclear. What was the original purpose of the Chinese construction? I doubt that they were using the binomial theorem.
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned;
The best lack all conviction, while the worst
Are full of passionate intensity.--Yeats
mastermindreader
View Profile
V.I.P.
Seattle, WA
12589 Posts

Profile of mastermindreader
Quote:
On 2013-04-12 07:16, spatlind wrote:
Quote:
On 2013-04-11 21:40, Woland wrote:
Then of course there is the depth and seriousness of Pascal's thought, and the rigor of his ascetic practice.



I'm not up to speed with Pascal's work or thoughts, with the exception of his wager. There doesn't, however, seem to me to have been much deep thinking put into that particular fallacy.


I'd suggest you actually read Pascal before jumping to that conclusion.
landmark
View Profile
Inner circle
within a triangle
4919 Posts

Profile of landmark
Quote:
On 2013-04-12 18:48, Magnus Eisengrim wrote:
Sorry I was unclear. What was the original purpose of the Chinese construction? I doubt that they were using the binomial theorem.

Pretty sophisticated--they were using it for computing square and cube roots. Omar Khayyam (yes, that one) also had a method for that, using the triangle. The following article shows how to compute square roots using the triangle--it involves defining and calculating what a row 1/2 would look like, and then applying the binomial expansion, though I don't know if this was the method the Chinese or Khayyam used:
http://en.citizendium.org/wiki/Pascal%27s_triangle
spatlind
View Profile
Special user
still moving
863 Posts

Profile of spatlind
Quote:
On 2013-04-12 18:58, mastermindreader wrote:

I'd suggest you actually read Pascal before jumping to that conclusion.


What makes you think I've not read his wager?
Actions lie louder than words - Carolyn Wells

I believe in God, only I spell it Nature - Frank Lloyd Wright.
tommy
View Profile
Eternal Order
Devil’s Island
16029 Posts

Profile of tommy
You either have or you haven't read Pascal's wager. Smile

If you have then the odds are you will go to heaven.
If there is a single truth about Magic, it is that nothing on earth so efficiently evades it.

Tommy
Woland
View Profile
Special user
680 Posts

Profile of Woland
Delighted that you have read Fragment 233, spatlind! Let's review and discuss it together. The Gutenberg project has a 1958 English translation, introduced by T.S. Eliot, that is accessible here.

The introductory part of the fragment goes like this:

Quote:
Infinite—nothing.—Our soul is cast into a body, where it finds number, time, dimension. Thereupon it reasons, and calls this nature, necessity, and can believe nothing else.

Unity joined to infinity adds nothing to it, no more than one foot to an infinite measure. The finite is annihilated in the presence of the infinite, and becomes a pure nothing. So our spirit before God, so our justice before divine justice. There is not so great a disproportion between our justice and that of God, as between unity and infinity.


The justice of God must be vast like His compassion. Now justice to the outcast is less vast, and ought less to offend our feelings than mercy towards the elect.

We know that there is an infinite, and are ignorant of its nature. As we know it to be false that numbers are finite, it is therefore true that there is an infinity in number. But we do not know what it is. It is false that it is even, it is false that it is odd; for the addition of a unit can make no change in its nature. Yet it is a number, and every number is odd or even (this is certainly true of every finite number). So we may well know that there is a God without knowing what He is. Is there not one substantial truth, seeing there are so many things which are not the truth itself?[Pg 66]

We know then the existence and nature of the finite, because we also are finite and have extension. We know the existence of the infinite, and are ignorant of its nature, because it has extension like us, but not limits like us. But we know neither the existence nor the nature of God, because He has neither extension nor limits.

But by faith we know His existence; in glory we shall know His nature. Now, I have already shown that we may well know the existence of a thing, without knowing its nature.


But the construction of the situation then begins, and I think this is where we can begin our discussion:

Quote:
Let us now speak according to natural lights.

If there is a God, He is infinitely incomprehensible, since, having neither parts nor limits, He has no affinity to us. We are then incapable of knowing either what He is or if He is. This being so, who will dare to undertake the decision of the question? Not we, who have no affinity to Him.

Who then will blame Christians for not being able to give a reason for their belief, since they profess a religion for which they cannot give a reason? They declare, in expounding it to the world, that it is a foolishness, stultitiam;[90] and then you complain that they do not prove it! If they proved it, they would not keep their word; it is in lacking proofs, that they are not lacking in sense. "Yes, but although this excuses those who offer it as such, and takes away from them the blame of putting it forward without reason, it does not excuse those who receive it." Let us then examine this point, and say, "God is, or He is not." But to which side shall we incline? Reason can decide nothing here. There is an infinite chaos which separated us. A game is being played at the extremity of this infinite distance where heads or tails will turn up. What will you wager? According to reason, you can do neither the one thing nor the other; according to reason, you can defend neither of the propositions.

Do not then reprove for error those who have made a choice; for you know nothing about it. "No, but I blame them for having made, not this choice, but a choice; for again both he who chooses heads and he who chooses tails are equally at fault, they are both in the wrong. The true course is not to wager at all."

Yes; but you must wager. It is not optional. You are embarked. Which will you choose then? Let us see. Since you must choose, let us see which interests you least. You have two things to lose, the true and the good; and two things to stake,[Pg 67] your reason and your will, your knowledge and your happiness; and your nature has two things to shun, error and misery. Your reason is no more shocked in choosing one rather than the other, since you must of necessity choose. This is one point settled. But your happiness? Let us weigh the gain and the loss in wagering that God is. Let us estimate these two chances. If you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation that He is.—"That is very fine. Yes, I must wager; but I may perhaps wager too much."—Let us see. Since there is an equal risk of gain and of loss, if you had only to gain two lives, instead of one, you might still wager. But if there were three lives to gain, you would have to play (since you are under the necessity of playing), and you would be imprudent, when you are forced to play, not to chance your life to gain three at a game where there is an equal risk of loss and gain. But there is an eternity of life and happiness. And this being so, if there were an infinity of chances, of which one only would be for you, you would still be right in wagering one to win two, and you would act stupidly, being obliged to play, by refusing to stake one life against three at a game in which out of an infinity of chances there is one for you, if there were an infinity of an infinitely happy life to gain. But there is here an infinity of an infinitely happy life to gain, a chance of gain against a finite number of chances of loss, and what you stake is finite. It is all divided; wherever the infinite is and there is not an infinity of chances of loss against that of gain, there is no time to hesitate, you must give all. And thus, when one is forced to play, he must renounce reason to preserve his life, rather than risk it for infinite gain, as likely to happen as the loss of nothingness.

For it is no use to say it is uncertain if we will gain, and it is certain that we risk, and that the infinite distance between the certainty of what is staked and the uncertainty of what will be gained, equals the finite good which is certainly staked against the uncertain infinite. It is not so, as every player stakes a certainty to gain an uncertainty, and yet he stakes a finite certainty to gain a finite uncertainty, without transgressing against reason. There is not an infinite distance between the certainty staked and the uncertainty of the gain; that is untrue. In truth, there is an infinity between the certainty of gain and the certainty of loss. But the uncertainty of the gain is proportioned to the certainty of the stake according to the[Pg 68] proportion of the chances of gain and loss. Hence it comes that, if there are as many risks on one side as on the other, the course is to play even; and then the certainty of the stake is equal to the uncertainty of the gain, so far is it from fact that there is an infinite distance between them. And so our proposition is of infinite force, when there is the finite to stake in a game where there are equal risks of gain and of loss, and the infinite to gain. This is demonstrable; and if men are capable of any truths, this is one.

"I confess it, I admit it. But, still, is there no means of seeing the faces of the cards?"—Yes, Scripture and the rest, etc. "Yes, but I have my hands tied and my mouth closed; I am forced to wager, and am not free. I am not released, and am so made that I cannot believe. What, then, would you have me do?"

True. But at least learn your inability to believe, since reason brings you to this, and yet you cannot believe. Endeavour then to convince yourself, not by increase of proofs of God, but by the abatement of your passions. You would like to attain faith, and do not know the way; you would like to cure yourself of unbelief, and ask the remedy for it. Learn of those who have been bound like you, and who now stake all their possessions. These are people who know the way which you would follow, and who are cured of an ill of which you would be cured. Follow the way by which they began; by acting as if they believed, taking the holy water, having masses said, etc. Even this will naturally make you believe, and deaden your acuteness.—"But this is what I am afraid of."—And why? What have you to lose?

But to show you that this leads you there, it is this which will lessen the passions, which are your stumbling-blocks.

The end of this discourse.—Now, what harm will befall you in taking this side? You will be faithful, honest, humble, grateful, generous, a sincere friend, truthful. Certainly you will not have those poisonous pleasures, glory and luxury; but will you not have others? I will tell you that you will thereby gain in this life, and that, at each step you take on this road, you will see so great certainty of gain, so much nothingness in what you risk, that you will at last recognise that you have wagered for something certain and infinite, for which you have given nothing.

"Ah! This discourse transports me, charms me," etc.

If this discourse pleases you and seems impressive, know[Pg 69] that it is made by a man who has knelt, both before and after it, in prayer to that Being, infinite and without parts, before whom he lays all he has, for you also to lay before Him all you have for your own good and for His glory, that so strength may be given to lowliness.


Personally, I think there is a lot of deep thinking packed into that little fragment, and I am not sure why you think it is a fallacy. I'd be delighted to hear more about it.
spatlind
View Profile
Special user
still moving
863 Posts

Profile of spatlind
It's quite simple really.

The wager seems to suggest that if god exists, then the reward is infinite. But this leaves out something very important, which is that to get the infinite reward, you must be judged. And if you are just betting in order to get the reward, then I think it's likely you'll be found out.
Actions lie louder than words - Carolyn Wells

I believe in God, only I spell it Nature - Frank Lloyd Wright.
tommy
View Profile
Eternal Order
Devil’s Island
16029 Posts

Profile of tommy
Gamblers don't go to heaven?
If there is a single truth about Magic, it is that nothing on earth so efficiently evades it.

Tommy
The Magic Cafe Forum Index » » Not very magical, still... » » Blaise Pascal (0 Likes)
[ Top of Page ]
All content & postings Copyright © 2001-2020 Steve Brooks. All Rights Reserved.
This page was created in 0.29 seconds requiring 5 database queries.
The views and comments expressed on The Magic Café
are not necessarily those of The Magic Café, Steve Brooks, or Steve Brooks Magic.
> Privacy Statement <

ROTFL Billions and billions served! ROTFL