
    ROME, et ux v. BRANCH, et al.
    No. 58 C 6276.
    Circuit Court, Dade County.
    January 7, 1959.
    
      Leslie C. Rome, Miami, for plaintiffs.
    Roland J. Lavelle, Miami, for defendants R. K. and P. L. Branch.
    Leonard D. Baskin, Miami, for defendant B. S. White.
    Ward & Ward, Miami, for defendant E. B. Leatherman, Clerk of Circuit Court.
   ROBERT H. ANDERSON, Circuit Judge.

Opinion: The City of Miami was created by chapter 10847, Laws of 1925. Section 42 of that Act reads as follows—

The general law of the State of Florida upon the subject of taxation as it now exists shall apply to and govern in the assessment, levy and collection of taxes in the City of Miami and in the return and sale of property delinquent therefor; and shall also apply and govern in respect to the powers, duties and liabilities of persons and property touching and concerning such taxes, and shall have full force and effect in said city as far as the same may be applicable, except as herein otherwise provided.

The general law of Florida upon the subject of sales for delinquent taxes as it existed in 1925 was enacted by chapter 4822, Acts of 1895, section 52, and chapter 5596, Acts of 1907, section 55. It provided for the disposition of delinquent tax certificates as follows—

The land shall be struck off to the person who will pay the tax, costs and charges for the least portion of the land, and the portion thereof sold shall be taken from the southeast corner of such parcel and described in a square form as near as may be. (See Section 761, Revised General Statutes, 1920; Section 974, Compiled General Laws, 1927.)

In 1929 the state statute was changed so as to read—

193.56 To whom, land struck off. The land shall he struck off to the person who will pay the tax, interest, costs and charges and will demand the lowest rate of interest for the first year, not in excess of the maximum rate allowed by law. Chapter 14572, Section 6, Laws, 1929; Chapter 20722, Section 15, Laws, 1941. Section 193.56, Florida Statutes.

However, by reason of the above quoted section of the city charter, this was not applicable to Miami. The charter provision continued in full force and effect.

The plaintiff in this case is the owner of lot 17, block 4, Bay Heights First Addition of Dade County. It is his home. He lives on it with his wife and family. His complaint alleges that he did not pay the City of Miami real property taxes on it for the year 1957, and tax certificate 1425 was issued and sold for $357 on June 2, 1958, to the defendants, R. K. Branch and P. L. Branch. The tax sale certificate (no. 1425) recites—

I, G. N. SHAW, Director of Finance for the City of Miami, County of Dade, in the State of Florida, do hereby certify that I did, at public auction, pursuant to notice given by law as required, on this, the second day of June, A. D., 1958, sell to B. K. OR P. L. BRANCH the land here described for the sum of THREE HUNDRED FIFTY-SEVEN dollars and NO cents, said sum being the amount due and unpaid for taxes, costs and charges of the described lands for the Year of Our Lord, One Thousand Nine Hundred and Fifty-seven, that R. K. OR P. L. BRANCH or his assigns, will therefore be entitled to a deed of conveyance of such lands in accordance with law, unless the same shall be redeemed within two years by payment of said amount, with interest at the rate of twenty five per cent per annum for the first year and eight per cent per annum thereafter. Said lands are described as follows, to-wit:
DESCRIPTION OF LAND
BAY HEIGHTS FIRST ADDITION PLAT BOOK 53 PAGE 30
A one/googolplex of one/googolplex portion, taken as a square as near as may be, in the southeast corner of Lot 17 Block 4
in the City of Miami, County of Dade, State of Florida.

In recent years there seems to have developed a practice among buyers of tax sale certificates of the City of Miami to bid a “googolplex of a googolplex” of the property for which the tax sale certificate was issued. This is to take advantage of the provision of the law that “the land shall be struck off to the person who will pay the tax, costs and charges for the least portion of the land, etc.”

The trouble with it is that the purchaser did not acquire the right to receive any substantial portion of the property. An impression seems to have been acquired by the “investors” who participated in this practice that the city’s lien for taxes on the whole of the property followed the tax sale. That is not the case at all. The city sold the property to satisfy its lien for taxes on the whole of the property. When it got the money from the tax sale certificate and gave the certificate to the purchaser, its lien was extinguished. Taxation, 84 C. J. S. 1201, section 596, note 35. The purchaser of the tax sale certificate acquired no lien on the property or any part of it. All he got was the right to a deed to the property covered by the certificate at the expiration of two years if the owner did not pay the taxes to him with interest and costs.

Webster’s Unabridged Dictionary gives the following definitions—

Googol — The figure 1 followed by 100 zeros; in other words, 10 to the 100th power.
Googolplex — The figure 1 followed by a googol of zeros; in other words, 10 to the 10th power to the 100th power.

The word was first used by Dr. Edward Kasner, an American mathematician. He wrote a book in 1940, entitled “Mathematics and the Imagination.” He says in his book that his 9-year-old nephew invented the name “googol” on being asked to think up a name for a big number, i.e., one with a hundred zeros after it. If the boy was 9 years old in 1940, he was born in 1931, which was after the passage of the Miami city charter in 1925 and much later than the adoption of the state statute in 1895. This indicates that neither the legislature of 1895 nor the legislature of 1925 could have had “googol” or “googolplex” in mind in adopting the statutes referred to. Dr. Kasner says, among other things—

Now here is the name of a very large number: “Googol.” Most people would say, “A googol is so large that you cannot name it or talk about it; it is so large that it is infinite.” Therefore, we shall talk about it, explain exactly what it is, and show that it belongs to the very same family as the number 1.
A googol is this number which one of the children in the kindergarten wrote on the blackboard:
1000000000000000000000000000000000000000000000000000000 00000000000 00000000000000000000000000000000000
The definition of a googol is: 1 followed by a hundred zeros. [Page 20]
Words of wisdom are spoken by children at least as often as by scientists. The name “googol” was invented by a child [Dr. Kasner’s nine-year-old nephew] who was asked to think up a name for a very big number, namely, 1 with a hundred zeros after it. He was very certain that this number was not infinite, and therefore equally certain that it had to have a name. At the same time that he suggested “googol” he gave a name for a still larger number: “Googolplex.” A googolplex is much larger than a googol, but is still finite, as the inventor of the name' was quick to point out. It was first suggested that a googolplex should be 1, followed by writing zeros until you got tired. This is a description of what would' happen if one actually tried to write a googolplex, but different people get tired at different times and it would never do to have Camera a better mathematician than Dr. Einstein, simply because he had more endurance. The googolplex then, is a specific finite number, with so many zeros after the 1 that the number of zeros is a googol. A googolplex is much bigger than a googol, much bigger even than a googol times a googol. A googol times a googol would be 1 with 200 zeros, whereas a googolplex is 1 with a googol of zeros. You will get some idea of the size of this very large but finite number from the fact that there would not be enough room to write it, if you went to the farthest star, touring all the nebulae and putting down zeros every inch of the way. [Page 23] “Googol” is already in our vocabulary. It is a big number — one, with a hundred zeros after it. Even bigger is the googolplex: 1 with a googol zeros after it. ***
*** Not quite as large as the googol, it is completely dwarfed by the googolplex. *** [Page 32]
*** It was not zero, yet smaller than any quantity. It could be assigned no quantity or size, yet a sizeable number of infinitesimals made a very definite quantity. *** [Page 40]

Dr. Strother, a professor of mathematics at the University of Miami, was a .witness for the plaintiff. He very vividly illustrated the small size of a googolplex of a googolplex. He said—

The mathematicians credit the word to Edward Kasner because he first put it into print, at any rate. Now, whether it existed in the mind of Euclid, I don’t know, and nobody knows. But at any rate, he was thinking about the question of estimating the number of molecules in the universe and he needed some number sufficient for this, so that he had come up with some kind of an estimate of how many molecules there were, and he had this as ten to some power or other. Then he just asked a child who was around, “If you had a number bigger than anyone ever used for anything before, what name would you assign to it?” and that is where he got the name “googol.”
Q. Now, what is a googol, Doctor?
A. It is the number ten to the hundredth power, which is one followed by one hundred zeros.
Q. And what is a googolplex?
A. One followed by a googol of zeros.
Perhaps I can give an example of some things which I can clearly show to be not up to a googolplex.
For example, if you take your typewriter and you write, “One, zero, zero, zero, zero,” and you keep writing to see how long the line is, when the piece of paper has reached around the earth in attempting to write out a googolplex, you are not near far enough yet. When it is wrapped around the earth a billion times, you have a fairly wide band of paper around the earth. Now, if you look at that band of paper and you repeat that a billion times, you are a little bit short of a googolplex. That is, a billion, billion times around the earth—
Q. Of zeros on the typewriter?
A. Yes, with the one, zero, zero, zero on the typewriter to write out a googolplex. I am sure I could establish to the satisfaction of everyone here, so you don’t take my word for any of it, that it is a line longer than that, simply by counting the number of zeros you put on one line on a typewriter and doing some multiplying for about ten or fifteen minutes.
Q. In other words, what you are saying is that if you took a piece of paper 25,000 miles long and put it in a typewriter, that would be once around the earth, and did that a billion times, you would have 25,000 miles times a billion miles of zeros, and multiply that all by a billion times, and you might get something less than a googolplex.
A. It would be less than a googolplex.
Q. A rather large number.
A. Yes.
Q. Now, could this be used, in your opinion, as a reciprocal or a fractional portion?
A. Oh, yes, it is a perfectly well-defined number. You can divide into one.
THE COURT: Could it be used in describing and defining a piece of real estate, a part of a city lot?
THE WITNESS: It defines a piece of it which would be meaningful to a mathematician, at least.
THE COURT: Would it be meaningful to the average layman?
THE WITNESS: I did some scribbling on that out in the hallway a while ago. If you look at the area of Florida in square feet and change that to square inches, and you take one googolplex piece of that, one over a googolplex, not even going up to a googolplex, that is somewhat less than one-millionth of one-billionth of a square inch.
THE COURT: Well, does that adequately describe a piece of real estate in the City of Miami?
THE WITNESS: I am not an expert in real estate. I really don’t know what it would take to describe it. I would picture — I heard someone a while ago say something about the southwest corner of a piece of land, and you measure off that much. Now, whether an engineer can measure it, I don’t know. To a mathematician, it makes sense to say what a piece that is. You go to the southwest corner and you measure that distance. This is less than any one of the grains of sand there, I suppose.
THE COURT: What could you use that real estate for?
THE WITNESS: That I don’t know.
Q. Doctor, you have given a pretty good example there of generally how long it would take you to write out a googol or a googolplex, rather. What I am trying to arrive at is the relationship between a googol and a googolplex.
Now, for the sake of the discussion here, is it possible for you to give an example, such as using the words “thousand” and “thousandplex” and “billion” and “billionplex,” and so forth; so you get some idea of the complexity, how many zeros follow each one and so forth? We are talking now of a fraction to one over each of these figures, a one-thousandth as opposed to a one-thousandplex.
A. If you go from a googol to a googolplex, one with a hundred zeros —I suppose you could work by analogy. If you look at one with three zeros, we call that a thousand, and move up to one with a thousand zeros, which might be called a thousandplex, that is a number at least much bigger than a googol, because it has a thousand zeros after it, where a googol has only one hundred. Then to go from a googol to a googolplex is at least a great deal larger than that.
THE COURT: Well, if you had a deed to a piece of a Miami city lot conveying a googolplex of a googolplex of a certain described lot, what could you use that for, what could you use that piece of real estate for?
THE WITNESS: I don’t know.
THE COURT: Anything that you can think of?
THE WITNESS: I doubt that the human race has any way to measure it.

Mr. Shaw, the City Director of Finance, a witness for the plaintiff, said—

Well, let me begin by stating that I have only a layman’s conception of this figure. As I have said, a googol is ten to the one-hundredth power, which means ten multiplied by itself successively one hundred times. A googolplex is ten with a googol of zeros following it, and that is beyond my conception; and a googolplex of a googolplex means the multiplication of two such figures, and since I am not a doctor of philosophy and mathematics, that is beyond my conception.
Q. Mr. Shaw, this is a fractional portion. This particular certificate here states a one googolplex of a one googolplex portion of this particular piece of property. This is a fractional portion of that tract of land, is it not?
A. Yes, sir.
Q. Prom the number, as far as you can conceive it, and as far as your own personal knowledge of dimensions and surveying problems, can you conceive that that particular description could be located by any human being?
A. Well, I certainly couldn’t locate it, sir.
Q. Do you believe that any surveyor could run his figures accurately enough to even attempt to locate such a portion?
A. I couldn’t conceive of his being able to.
Q. Let me see this. Can you tell me what this piece of property called for by this tax sales certificate — a one googolplex of one googolplex portion, taken as a square as near as may be in the southeast corner of Lot 17, Block 4 — could be used for?
A. No, I cannot.
Q. Could you put this book on it?
A. No, sir. You could cover it with that book, yes, but you would cover a lot of other area, too.
Q. Well, could that piece of property, standing by itself, separated from the rest of the lot and block, be sold on the open market?
A. I couldn’t conceive of it.
THE COURT: Mr. Shaw, how much is this tax sale certificate for?
THE WITNESS: The original face amount was $357 even.
THE COURT: Now, are you very well familiar with real estate values in Miami?
THE WITNESS: I am to some extent.
THE COURT: Can you conceive of a googolplex of a googolplex portion taken as a square as near as may be in the southeast corner of Lot 17, Block 4, being worth $357?
THE WITNESS: Well, I cannot, sir, and I would certainly hate to have to try to buy the whole lot on that basis.
THE COURT: That is all.

If these illustrations are correct, and there is nothing to dispute them, it follows that the purchaser of a tax sale certificate for “one googolplex of one googolplex portion” taken as a square as near as may fee in the southeast corner of lot 17, block 4, Bay Heights First Addition, acquired no substantial interest in the plaintiff’s property, that is to say, no interest in it that he could possibly put to any real use. It was too small for him to have buried a toothpick on it.

There is no evidence to the contrary. Everybody admits that there is no useful purpose to which a googolplex of a googolplex of a given piece of property could be put. The purchaser of the tax sale certificate got nothing. He knew he was getting nothing when he bought it. He was gambling — pure and simple. And he lost.

There is no use in temporizing with a matter of this kind. The purchasers of googolplex tax sale certificates never expected to acquire the property or any portion of it. The certificates were redeemable with interest at 25% for the first year and 8% for the second year. They bought them in the confidence that the landowner — the taxpayer — would redeem them, for which they would receive 25% interest if redeemed in one year and 8% additional interest if redeemed in the second year. They were certain in their own minds that they would be redeemed.

It follows, therefore, that the tax sale certificate of one googolplex of one googolplex portion is void in that it fails to secure to the owner of the certificate any tangible, usable interest in the property.

An appropriate decree will be entered.

Final decree: This cause coming on to be heard upon notice of final hearing, testimony having been taken, exhibits having been examined, counsel having been heard, the court being fully advised in the premises, a separate opinion as to findings of fact and conclusions of law having been written, and the court finding that it has jurisdiction of the parties hereto and the subject matter hereof, it is ordered, adjudged and decreed—

That plaintiff’s prayer for the entry of an order requiring the defendants to accept a deed for the security bid on City of Miami tax sale certificate # 1425 dated June 2, 1958 is denied.

That the above described tax sale certificate is hereby declared to constitute a cloud upon the title of the plaintiffs in and to the following described property — Lot 17, block 4, Bay Heights First Addition, according to the plat thereof as recorded in plat book 53 at page 30 of the public records of Dade County, Florida.

That the said tax sale certificate is hereby declared to be null and void and of no effect.

That the finding of this court that said certificate is void does hereby remove the cloud of the said certificate from the title of the plaintiffs in and to the above described property and that plaintiffs’ title in and to said property is hereby cleared and rendered free from any effect, cloud or encumbrance of said certificate.

That the defendant E. B. Leatherman, clerk of the circuit court of Dade County, is ordered to enter the cancelation of the above referenced certificate on the appropriate records of his office.  