Home > All, Books, Education, Science > Finally Finished "A Tour Of The Calculus" By David Berlinski

Finally Finished "A Tour Of The Calculus" By David Berlinski

I’ll start out by referring you to a previous post where I wrote about David Berlinski and his Creationist math problems. This was my introduction to Berlinski and his philosophy of mathematics – how it should be used to calculate the odds of evolution happening; that small odds is proof that something didn’t happen. And by that logic, no one could win the lottery because the odds are so small.

I tried not to let his bad logic interfere with my reading of A Tour Of The Calculus, and I think I did a pretty good job. I actually enjoyed this book.

Overall, it’s very well written. It’s easy to follow. He is very narrative and eloquent in his writing.

My only problem with the book, and it really isn’t a problem, is that it isn’t really for someone who has no experience with calculus at all. The first half may be alright for the beginner, but when he starts talking about the integral and differentiation, I feel like he makes some grand assumptions about his reader – that they understand these concepts to begin with. I found myself struggling with the equations and ideas that he presented simply because I didn’t understand the processes involved in integration, differentiation and the like.

I also understand that you couldn’t possibly encompass the entirety of the calculus in a 300-page book. I suppose it’s more a problem of time and space than it is of incompetency of the writer.

Personally, I would absolutely recommend this book for someone who is experienced with calculus, but hasn’t touched it in a long time. It would be a great refresher course.

To conclude with, Berlinski doesn’t bring up any Creationism or Anti-Evolution rhetoric in this book, which I was somewhat surprised with. Usually Creationists love to inject their religion in everything they do. So congratulations to Berlinski on a great book.

And, as usual… read a book. It’s good for you.

Categories: All, Books, Education, Science
  1. Bret
    Monday July 14, 2008 at 5:53 PM


    I am curious to know your feelings on origin?

  2. Tuesday July 15, 2008 at 4:43 AM

    Are you speaking about the origin of life? If you are, I have to say that I don’t know. We don’t know how life came about yet.

    And personally, that’s one of the beauties of science. It’s ok to say that you don’t know… yet. Science is always looking for the answers.

    And that is not how religion works. Religion works from the base assumption that they know everything to begin with. And what happens if some portion of a religion is proven to be wrong? Their whole system collapses.

    What happens when something in science is proven wrong? We celebrate! We’ve learned something new about our universe.

    That basically sums up my feelings about the origin of life. I don’t know enough about it to comment. It’s too easy and intellectually lazy to say God did it.

  3. Bret
    Tuesday July 15, 2008 at 9:16 PM

    Thanks for replying.. Has science ever been able to produce “anything” from “nothing”. In other words, can something just pop into existence?

  4. Bret
    Tuesday July 15, 2008 at 9:46 PM

    Also curious about your opinion on this:

    Alan Lightman, a MIT professor, said in his book Origins: The Lives and Worlds of Modern Cosmologists (Harvard University Press, 1990), “Contrary to popular myths, scientists appear to have the same range of attitudes about religious matters as does the general public.”

    This fact can be established either from anecdote or from statistical data. Sigma Xi, the scientific honorary society, ran a large poll a few years ago which showed that, on any given Sunday, around 46 percent of all Ph.D. scientists are in church; for the general population the figure is 47 percent. So, whatever influences people in their beliefs about God, it doesn’t appear to have much to do with having a Ph.D. in science

  5. Wednesday July 16, 2008 at 5:31 AM

    There is a difference between science and scientists. Yes, there are scientists who believe in God – it is a compartmentalization of knowledge… they separate their beliefs from their work.

    Whether or not a certain type of person (scientist) believes in a God does not give it truth value. What does the evidence point to? If I were to base my belief in God on what other people thought, that would be a logical fallacy; the argument from authority… not based on any factual information – only the authority of another’s opinion – minus the evidence.

    Has science ever been able to produce “anything” from “nothing”. In other words, can something just pop into existence?

    You’re largely basing this question on a major unstated premise… you feel that the Universe should act in accordance with your intuition. You feel that it doesn’t make sense for something to “pop into existence.” It is counter-intuitive. And so is quantum mechanics. Nothing about quantum mechanics behaves according to what is intuitive.

    Human intuition means nothing when it comes to understanding our Universe. We have to base what we know on where the evidence points… not to where our feelings direct us. That’s how we ended up believing that lightening came from an angry God throwing those bolts at us. Or that diseases were punishments for bad behavior in the eyes of “God.” Science has taught us better than to trust our intuition.

  6. Bret
    Wednesday July 16, 2008 at 7:30 AM

    I am not asking you what you think of the scientist, I am asking what you think of science based theroems like Donald Page’s, who states that the randomness of the universes and our existence is so great , 10,000,000,000 to the 24th, that is virtually impossible.

  7. Wednesday July 16, 2008 at 12:50 PM

    Given an infinite amount of “time” for that 10 to the 24th to come about, it’s pretty much guaranteed to happen.

    Talking about odds of something happening is not a good argument against a claim. Like I’d mentioned in my previous post about Berlinski (this is the same logic he uses), using the “odds argument” is no different than the guy at the lottery claims office telling you that you didn’t win because the odds are too great that you didn’t… without even looking at your ticket.

    You’ve matched all the numbers according to what was drawn – yet the prize official determines that you didn’t win because of the “odds of winning.”

    It’s like walking down the street, looking at a person and saying, “Wow, what are the odds of seeing that person right there, wearing that particular outfit, saying precisely what they’re saying right now, with that particular person they’re walking with, and the weather being precisely what it is right now, with that precise car driving by, with that exact license plate number… the odds are too great for that to happen – therefore, what I’m seeing isn’t real. God must have done it.

    That’s my take on the “odds argument.” It’s invalid. Completely illogical – post hoc reasoning.

  8. Bret
    Wednesday July 16, 2008 at 5:13 PM

    Ok now take those coincidences out 10,000,000,000 to the 24th, then I guess you have an analogy.

  9. Wednesday July 16, 2008 at 6:10 PM

    And that’s exactly what that type of logic does. It takes a situation, works out the odds and says it can’t happen… even though it already did happen.

    What are the odds of me replying back to you right at this very instant. Well, let’s figure it out. Let’s break down the interval of time into 10,000,000,000 x 10 to the 24th. At that very instant is when I hit the “Submit Comment” button. But, according to your logic, I couldn’t have replied back because of the odds.

    I am replying back at 7:10pm and .2 x 10,000,000,000 x 10 to the -24th power seconds.

    But, according to your logic, I didn’t reply back because the odds are against it.

    You can infinitely break time down into smaller and smaller intervals until you reach this large number you’re speaking of. And if we follow the “odds logic,” then nothing at all could ever happen because the odds are against it.

    Odds are not a function of reality. They are a guess. No one would win the lottery if it was actually dependent upon odds.

    But, if we want to be consistent with “odds logic,” and a Universe of our complexity requires such a large number to bring it into existence… then how much GREATER must the odds be against a magical invisible man just “popping into existence?” An invisible man who just happens to be omnifarious? Omnific? A being capable of all of this, an intelligent being with all of these traits just randomly just popping into existence?

    I would guess that you would have to take your odds of our Universe “popping into existence,” your “10,000,000,000 x 10 to the 24th” and at least cube it. Especially when there is no evidence of that invisible man even existing… let alone magic spells and incantations that would bring a Universe into existence.

    Don’t forget about the Cosmic Microwave Background… why would God create resonance from a “Big Bang” if He just wished the Universe into existence? What are the odds?

  10. Bret
    Thursday July 17, 2008 at 8:53 AM

    Ok, so just to understand your two analogies:

    you compare meeting a person on the street with a few specific criteria to the origin of the universe, and the chance of replying at a specific time to my comment -which you maintain is equivalent to 10,000,000,000 x 10 to the 24th.

    Got it, thanks.

  11. Bret
    Thursday July 17, 2008 at 10:48 AM

    Oops I left out one of your other analogies:

    You compare winning the lottery to the the odds of 10,000,000,000 -to the 124th.

    Lets see, the if and it never has happened, every man women and child in America bought a lottery ticket the odd would be 1:300,000,000.

    But the origin of the universe odds are

    Thats just for the exsitence of the universe. Better go buy a lotto ticket – quick

    Fred Hoyles and NC Wickramasingle conclude the odds of the random formation of a single enzyme from amino acids is 10 to the 40,000…thats just a tiny tiny part in the formation of life.

  12. Thursday July 17, 2008 at 12:23 PM

    And yet, you still haven’t acknowledged the fact that your invisible man would have to “pop into existence” with all of the traits of a living being (in addition to being INVISIBLE and filled with MAGICAL POWERS).

    My model requires complex things to generate over long periods of time, to go from simple to complex over long periods of time – in a logical, if from a counter-intuitive sequence.

    Your model, on the other hand, requires that the most complex (the invisible man with magical powers) comes FIRST. And from there, he creates a Universe which seems as though it evolved from the simple to the complex. You couldn’t even begin to try to calculate the “odds” of that happening.

    In fact, I’m willing to bet that your scenario is physically impossible – no odds at all… but you admit my scenario IS possible.

    Occam’s Razor does a fine job of working out that problem.

    Odds schmodds. It means nothing. It’s a number. That number is only there to give you some intellectual cover for accepting an invisible man with magical abilities as the creator of everything.

  13. Thursday July 17, 2008 at 4:14 PM

    As a final comment on this debate, as I’ve said before, odds are an estimate… a guess.

    Probability cannot be used as proof of a claim – or against a claim for that matter.

    If you want to say that our Universe only had a certain probability of coming into existence by natural means, that’s great. BUT, you cannot use those odds as proof against the Universe coming into existence by those means.

    That would require actual evidence. And, sufficed to say, the evidence points toward a natural “popping into of existence.”

    You’ve not offered any evidence. Only “odds.” That proves nothing.

    When someone goes to the lottery official to claim their prize, does the official even MENTION odds of winning? No, he looks at the EVIDENCE… the numbers on the winning ticket. Do they match what was drawn? Yes? Then the person wins, regardless of the “odds.”

    Same applies to our Universe. We could waste our time thinking about “odds.” But, why not put our attention toward something more fruitful, like looking at the actual evidence.?

    Would you bring up odds in a courtroom? Would a prosecutor ask what the “odds were” that the defendant killed someone? No. Don’t be foolish.

    The prosecutor would offer EVIDENCE. Proof of what he was claiming.

    I’m willing to bet that even if the odds were 1 in 2, you’d still be using the same arguments you’re using right now. It’s simply an ideological excuse for denying science.

    You’ve no interest in Truth… the “odds argument” is simply an obfuscation, a distraction from the real issue… proof.

  14. Thursday July 24, 2008 at 7:25 AM

    Is there a free e-book?


    Haaay, calculus, why oh why?


    I’d love to read that. I’ll try to look for that book.



  15. phil
    Tuesday August 17, 2010 at 9:19 PM

    that book was awful… he went on so many unecessary tangents. His book was like a mathematical twilight. I would much rather have read a textbook, at least its straight forward

  16. Charles Brown
    Friday May 11, 2012 at 11:41 AM

    think! Berlinski is not says because the odds are against evolution it could not have happened; he’s saying what odds tell us all the time. It most likely did not happen. (probably Also, if we realy think! we would know that even before the big bang, there had to have been energy, laws of motion, and all of hte dynames that we know as physics, cooling, heat, compression, gravity, where did these things come from? Nothing? If we think these things came from nothing then that’s not science that’s wishful thinking, that’s philosophy….. think!

    • Friday May 25, 2012 at 6:54 PM

      See, the problem is that statistics isn’t meant to answer questions like that. It’s only about probability. The odds of winning the lottery might be 1 in 250,000,000, but guess what, someone always wins. Odds say nothing about an event after the fact. It’s completely irrelevant.

  17. John C. Redman
    Saturday December 8, 2012 at 4:29 PM

    Godkillzyou doesn’t apply his own logis to his position, which appears to be the logic of huge numbers and infinite amounts of time can producing anything no matter how unlikely.. It may be the case, and who knows could even produce ……God.

  1. Friday July 18, 2008 at 4:18 AM

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